13447:
198:
4350:
3945:
13433:
39:
13471:
6438:
13459:
182:
4345:{\displaystyle \operatorname {R} _{\mathbf {X} \mathbf {X} }={\begin{bmatrix}\operatorname {E} &\operatorname {E} &\cdots &\operatorname {E} \\\\\operatorname {E} &\operatorname {E} &\cdots &\operatorname {E} \\\\\vdots &\vdots &\ddots &\vdots \\\\\operatorname {E} &\operatorname {E} &\cdots &\operatorname {E} \\\\\end{bmatrix}}}
8159:
5294:
5108:
6169:
2075:
7990:
5626:
5113:
4927:
4912:
4824:
9948:
at the satellites, and the point of time at the receiver on the ground. This is done by the receiver generating a replica signal of the 1,023-bit C/A (Coarse/Acquisition) code, and generating lines of code chips in packets of ten at a time, or 10,230 chips (1,023 Ă 10), shifting slightly as it goes
8437:
the autocorrelation for other lag values being zero. In this calculation we do not perform the carry-over operation during addition as is usual in normal multiplication. Note that we can halve the number of operations required by exploiting the inherent symmetry of the autocorrelation. If the signal
8866:
9549:, then form a function which is a valid autocorrelation in the sense that it is possible to define a theoretical process having exactly that autocorrelation. Other estimates can suffer from the problem that, if they are used to calculate the variance of a linear combination of the
1180:
2332:
6109:
6433:{\displaystyle {\begin{aligned}R_{ff}(\tau )&=\lim _{T\rightarrow \infty }{\frac {1}{T}}\int _{0}^{T}f(t+\tau ){\overline {f(t)}}\,{\rm {d}}t\\R_{yy}(\ell )&=\lim _{N\rightarrow \infty }{\frac {1}{N}}\sum _{n=0}^{N-1}y(n)\,{\overline {y(n-\ell )}}.\end{aligned}}}
1772:
9647:. The Durbin-Watson can be linearly mapped however to the Pearson correlation between values and their lags. A more flexible test, covering autocorrelation of higher orders and applicable whether or not the regressors include lags of the dependent variable, is the
1185:
Note that this expression is not well defined for all-time series or processes, because the mean may not exist, or the variance may be zero (for a constant process) or infinite (for processes with distribution lacking well-behaved moments, such as certain types of
10930:
Kalvani, Payam Rajabi; Jahangiri, Ali Reza; Shapouri, Samaneh; Sari, Amirhossein; Jalili, Yousef Seyed (August 2019). "Multimode AFM analysis of aluminum-doped zinc oxide thin films sputtered under various substrate temperatures for optoelectronic applications".
2913:
5903:
The above definitions work for signals that are square integrable, or square summable, that is, of finite energy. Signals that "last forever" are treated instead as random processes, in which case different definitions are needed, based on expected values. For
1684:
3570:
3318:
1338:: the autocovariance depends only on the time-distance between the pair of values but not on their position in time. This further implies that the autocovariance and autocorrelation can be expressed as a function of the time-lag, and that this would be an
3446:
3193:
2505:
9167:
3874:
6866:
6739:
5308:, the above definition is often used without the normalization, that is, without subtracting the mean and dividing by the variance. When the autocorrelation function is normalized by mean and variance, it is sometimes referred to as the
4454:
2590:
8683:
5450:
2677:
4829:
4741:
7719:
8154:{\displaystyle {\begin{array}{rrrrrr}&2&3&-1\\\times &2&3&-1\\\hline &-2&-3&1\\&&6&9&-3\\+&&&4&6&-2\\\hline &-2&3&14&3&-2\end{array}}}
6875:
In the following, we will describe properties of one-dimensional autocorrelations only, since most properties are easily transferred from the one-dimensional case to the multi-dimensional cases. These properties hold for
2160:
5913:
801:
9932:
that results from the motion of the particles. Autocorrelation of the signal can be analyzed in terms of the diffusion of the particles. From this, knowing the viscosity of the fluid, the sizes of the particles can be
5289:{\displaystyle \operatorname {K} _{\mathbf {Z} \mathbf {Z} }=\operatorname {E} )(\mathbf {Z} -\operatorname {E} )^{\rm {H}}]=\operatorname {R} _{\mathbf {Z} \mathbf {Z} }-\operatorname {E} \operatorname {E} ^{\rm {H}}}
5103:{\displaystyle \operatorname {K} _{\mathbf {X} \mathbf {X} }=\operatorname {E} )(\mathbf {X} -\operatorname {E} )^{\rm {T}}]=\operatorname {R} _{\mathbf {X} \mathbf {X} }-\operatorname {E} \operatorname {E} ^{\rm {T}}}
5898:
1486:
9616:. Problematic autocorrelation of the errors, which themselves are unobserved, can generally be detected because it produces autocorrelation in the observable residuals. (Errors are also known as "error terms" in
4571:
11119:
7987:) by hand, we first recognize that the definition just given is the same as the "usual" multiplication, but with right shifts, where each vertical addition gives the autocorrelation for particular lag values:
905:
7558:
7827:
2736:
4605:
3780:
3653:
3452:
3199:
6442:
These definitions have the advantage that they give sensible well-defined single-parameter results for periodic functions, even when those functions are not the output of stationary ergodic processes.
9523:
1747:
8607:
3331:
9443:
3080:
9013:
8688:
6174:
5918:
8519:
7120:
2391:
9020:
7243:
7022:
6949:
1501:
2719:
2070:{\displaystyle \rho _{XX}(t_{1},t_{2})={\frac {\operatorname {K} _{XX}(t_{1},t_{2})}{\sigma _{t_{1}}\sigma _{t_{2}}}}={\frac {\operatorname {E} \left}{\sigma _{t_{1}}\sigma _{t_{2}}}}.}
10999:
8435:
7948:
8356:
3036:
2382:
6748:
6621:
10402:
8233:
10221:
4385:
2510:
1231:
402:
9808:
7427:
5667:
4712:
824:
2602:
1386:
9727:(MA), the autocorrelation function is used to determine the appropriate number of lagged error terms to be included. This is based on the fact that for an MA process of order
578:
9764:
7585:
10271:
8281:
7466:
5389:
4484:
4374:
3905:
3701:
9303:
9242:
1282:
9869:
9843:
7874:
2107:
140:
10303:
9702:
4631:
3935:
3679:
6522:
3804:
1764:. However, in other disciplines (e.g. engineering) the normalization is usually dropped and the terms "autocorrelation" and "autocovariance" are used interchangeably.
543:
271:
7981:
6542:
2954:
9195:
7341:
3069:
327:
Different fields of study define autocorrelation differently, and not all of these definitions are equivalent. In some fields, the term is used interchangeably with
7277:
7169:
5768:
5442:
4663:
2994:
1336:
1309:
897:
870:
676:
649:
485:
9651:. This involves an auxiliary regression, wherein the residuals obtained from estimating the model of interest are regressed on (a) the original regressors and (b)
9276:
9215:
5797:
5700:
5621:{\displaystyle R_{ff}(\tau )=\int _{-\infty }^{\infty }f(t+\tau ){\overline {f(t)}}\,{\rm {d}}t=\int _{-\infty }^{\infty }f(t){\overline {f(t-\tau )}}\,{\rm {d}}t}
5422:
5350:
1255:
9342:
245:
8630:
7723:
When mean values are subtracted from signals before computing an autocorrelation function, the resulting function is usually called an auto-covariance function.
4907:{\displaystyle \mathbf {a} ^{\mathrm {H} }\operatorname {R} _{\mathbf {Z} \mathbf {Z} }\mathbf {a} \geq 0\quad {\text{for all }}\mathbf {a} \in \mathbb {C} ^{n}}
4819:{\displaystyle \mathbf {a} ^{\mathrm {T} }\operatorname {R} _{\mathbf {X} \mathbf {X} }\mathbf {a} \geq 0\quad {\text{for all }}\mathbf {a} \in \mathbb {R} ^{n}}
10183:
10159:
9567:
9547:
9362:
8945:
7361:
7307:
7140:
7042:
6614:
6499:
6479:
6155:
6135:
5748:
5720:
2974:
618:
598:
513:
442:
422:
6594:
2142:
300:
as a function of the time lag between them. The analysis of autocorrelation is a mathematical tool for finding repeating patterns, such as the presence of a
168:
2337:
The normalization is important both because the interpretation of the autocorrelation as a correlation provides a scale-free measure of the strength of
11127:
7471:
8861:{\displaystyle {\begin{aligned}F_{R}(f)&=\operatorname {FFT} \\S(f)&=F_{R}(f)F_{R}^{*}(f)\\R(\tau )&=\operatorname {IFFT} \end{aligned}}}
10130:). In particular, it is possible to have serial dependence but no (linear) correlation. In some fields however, the two terms are used as synonyms.
6164:, the expectation can be replaced by the limit of a time average. The autocorrelation of an ergodic process is sometimes defined as or equated to
684:
5805:
12568:
9598:
10992:
10967:
10609:
Colberg, P.; Höfling, F. (2011). "Highly accelerated simulations of glassy dynamics using GPUs: caveats on limited floating-point precision".
7995:
13073:
10721:
Percival, Donald B. (1993). "Three
Curious Properties of the Sample Variance and Autocovariance for Stationary Processes with Unknown Mean".
10023:, is used by X-ray diffractionists to help recover the "Fourier phase information" on atom positions not available through diffraction alone.
1694:
1397:
4496:
1175:{\displaystyle \operatorname {K} _{XX}(t_{1},t_{2})=\operatorname {E} \left=\operatorname {E} \left-\mu _{t_{1}}{\overline {\mu }}_{t_{2}}}
13223:
9620:.) Autocorrelation of the errors violates the ordinary least squares assumption that the error terms are uncorrelated, meaning that the
12847:
11488:
2327:{\displaystyle \rho _{XX}(\tau )={\frac {\operatorname {K} _{XX}(\tau )}{\sigma ^{2}}}={\frac {\operatorname {E} \left}{\sigma ^{2}}}}
7746:
6104:{\displaystyle {\begin{aligned}R_{ff}(\tau )&=\operatorname {E} \left\\R_{yy}(\ell )&=\operatorname {E} \left.\end{aligned}}}
12621:
4576:
161:
3716:
3589:
13060:
130:
217:
is 1.0, the value of the result at 5 different points is indicated by the shaded area below each point. Also, the symmetry of
95:
9960:
intensity of a nanostructured system is the
Fourier transform of the spatial autocorrelation function of the electron density.
11072:
11048:
10914:
10775:
10705:
10518:
10476:
10445:
10361:
9888:
9448:
9644:
9612:(OLS), the adequacy of a model specification can be checked in part by establishing whether there is autocorrelation of the
8528:
105:
11483:
11183:
9374:
5905:
12087:
11235:
9594:
8950:
154:
8441:
7151:
The continuous autocorrelation function reaches its peak at the origin, where it takes a real value, i.e. for any delay
2908:{\displaystyle \left|\operatorname {R} _{XX}(t_{1},t_{2})\right|^{2}\leq \operatorname {E} \left\operatorname {E} \left}
10672:
10593:
10568:
10543:
10471:
Kun Il Park, Fundamentals of
Probability and Stochastic Processes with Applications to Communications, Springer, 2018,
9613:
6877:
100:
7053:
12870:
12762:
11136:
7829:
can be used when the signal size is small. For example, to calculate the autocorrelation of the real signal sequence
1679:{\displaystyle \operatorname {K} _{XX}(\tau )=\operatorname {E} \left=\operatorname {E} \left-\mu {\overline {\mu }}}
3565:{\displaystyle S_{XX}(f)=\int _{-\infty }^{\infty }\operatorname {R} _{XX}(\tau )\cos(2\pi f\tau )\,{\rm {d}}\tau .}
3313:{\displaystyle S_{XX}(f)=\int _{-\infty }^{\infty }\operatorname {R} _{XX}(\tau )e^{-i2\pi f\tau }\,{\rm {d}}\tau .}
13475:
13048:
12922:
10748:
10387:
10371:
7174:
6960:
6887:
13106:
12767:
12512:
11883:
11473:
10611:
10008:
effect or to fix intonation). When applied at time scales larger than a second, autocorrelation can identify the
5722:
in the integral is a dummy variable and is only necessary to calculate the integral. It has no specific meaning.
1761:
366:
296:
with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations of a
10089:) it can be used to compute an autocorrelation seismic attribute, out of a 3D seismic survey of the underground.
2682:
13157:
12369:
12176:
12065:
12023:
10335:
10100:
7259:
The autocorrelation of the sum of two completely uncorrelated functions (the cross-correlation is zero for all
3441:{\displaystyle \operatorname {R} _{XX}(\tau )=\int _{-\infty }^{\infty }S_{XX}(f)\cos(2\pi f\tau )\,{\rm {d}}f}
2341:, and because the normalization has an effect on the statistical properties of the estimated autocorrelations.
2152:
12097:
8361:
7879:
3188:{\displaystyle \operatorname {R} _{XX}(\tau )=\int _{-\infty }^{\infty }S_{XX}(f)e^{i2\pi f\tau }\,{\rm {d}}f}
13507:
13400:
12359:
11262:
8285:
3011:
2730:
2357:
1234:
309:
9953:
in the incoming satellite signal, until the receiver replica signal and the satellite signal codes match up.
9529:
The advantage of estimates of the last type is that the set of estimated autocorrelations, as a function of
12951:
12900:
12885:
12875:
12744:
12616:
12583:
12409:
12364:
12194:
10376:
9957:
9672:
8166:
6450:
4735:
10191:
9525:
separately and calculating separate sample means and/or sample variances for use in defining the estimate.
1201:
372:
13463:
13295:
13096:
13020:
12321:
12075:
11744:
11208:
9769:
9640:
9629:
8660:
3323:
3322:
For real-valued functions, the symmetric autocorrelation function has a real symmetric transform, so the
3005:
369:
between values of the process at different times, as a function of the two times or of the time lag. Let
293:
9971:, autocorrelation is used to establish a link between surface morphology and functional characteristics.
7366:
5634:
4668:
809:
13502:
13180:
13152:
13147:
12895:
12654:
12560:
12540:
12448:
12159:
11977:
11460:
11332:
10127:
9921:
2500:{\displaystyle \operatorname {R} _{XX}(t_{1},t_{2})={\overline {\operatorname {R} _{XX}(t_{2},t_{1})}}}
1345:
30:
9162:{\displaystyle {\hat {R}}(k)={\frac {1}{(n-k)\sigma ^{2}}}\sum _{t=1}^{n-k}(X_{t}-\mu )(X_{t+k}-\mu )}
12912:
12680:
12401:
12326:
12255:
12184:
12104:
12092:
11962:
11950:
11943:
11651:
11372:
10382:
10325:
10001:
9968:
9713:
3704:
551:
488:
305:
9734:
6449:
can be treated by a short-time autocorrelation function analysis, using finite time integrals. (See
13497:
13395:
13162:
13025:
12710:
12675:
12639:
12424:
11866:
11775:
11734:
11646:
11337:
11176:
10977:
10697:
10230:
10162:
10075:
10027:
9917:
9676:
9648:
9621:
8238:
7432:
7246:
5355:
338:
60:
4461:
4357:
3882:
3684:
13304:
12917:
12857:
12794:
12432:
12416:
12154:
12016:
12006:
11856:
11770:
10366:
10320:
9910:
9281:
9220:
7573:
3869:{\displaystyle \operatorname {R} _{\mathbf {X} \mathbf {X} }\triangleq \ \operatorname {E} \left}
3681:
matrix containing as elements the autocorrelations of all pairs of elements of the random vector
1260:
135:
70:
11040:
11033:
9848:
9813:
8525:) where the left and right tails of the previous autocorrelation sequence will overlap and give
7832:
2082:
13342:
13272:
13065:
13002:
12757:
12644:
11641:
11538:
11445:
11324:
11223:
10850:"Analytical form of the autocorrelation function for the fluorescence correlation spectroscopy"
10315:
10276:
9680:
9609:
8871:
8675:
7736:
6861:{\displaystyle R_{ff}(\tau )\triangleq \int _{t_{0}}^{t_{0}+T}f(t){\overline {f(t-\tau )}}\,dt}
6734:{\displaystyle R_{ff}(\tau )\triangleq \int _{t_{0}}^{t_{0}+T}f(t+\tau ){\overline {f(t)}}\,dt}
4610:
3914:
3658:
2338:
346:
342:
55:
10692:
Spectral
Analysis for Physical Applications: Multitaper and Conventional Univariate Techniques
6504:
1284:
are time-independent, and further the autocovariance function depends only on the lag between
521:
250:
13367:
13309:
13252:
13078:
12971:
12880:
12606:
12490:
12349:
12341:
12231:
12223:
12038:
11934:
11912:
11871:
11836:
11803:
11749:
11724:
11679:
11618:
11578:
11380:
11203:
11128:
Quantitative Data
Processing in Scanning Probe Microscopy: SPM Applications for Nanometrology
10273:
would imply that there is statistical dependence between all pairs of values at the same lag
9602:
7953:
6527:
4449:{\displaystyle \operatorname {R} _{\mathbf {Z} \mathbf {Z} }\triangleq \ \operatorname {E} .}
4377:
2933:
2585:{\displaystyle \operatorname {R} _{XX}(\tau )={\overline {\operatorname {R} _{XX}(-\tau )}}.}
492:
10689:
9174:
7316:
3044:
13290:
12865:
12814:
12790:
12752:
12670:
12649:
12601:
12480:
12458:
12427:
12336:
12213:
12164:
12082:
12055:
12011:
11967:
11729:
11505:
11385:
11095:
10861:
10804:
10629:
10341:
10126:
is closely linked to the notion of autocorrelation, but represents a distinct concept (see
9724:
9624:
does not apply, and that OLS estimators are no longer the Best Linear
Unbiased Estimators (
9590:
9586:
9582:
8522:
7262:
7154:
5753:
5427:
5321:
4636:
2979:
2927:
1757:
1314:
1287:
875:
848:
654:
627:
463:
9305:
are replaced by the standard formulae for sample mean and sample variance, then this is a
9261:
9200:
5773:
5676:
5398:
5326:
2672:{\displaystyle \left|\operatorname {R} _{XX}(\tau )\right|\leq \operatorname {R} _{XX}(0)}
1240:
8:
13437:
13362:
13285:
12966:
12730:
12723:
12685:
12593:
12573:
12545:
12278:
12144:
12139:
12129:
12121:
11939:
11900:
11790:
11780:
11689:
11468:
11424:
11342:
11267:
11169:
10690:
9975:
9578:
9321:
4487:
831:
224:
11099:
10865:
10808:
10633:
10071:, spatial autocorrelation refers to correlation of a variable with itself through space.
10045:
to score the similarity of an observed spectrum to an idealized spectrum representing a
10026:
In statistics, spatial autocorrelation between sample locations also helps one estimate
8612:
13451:
13262:
13116:
13012:
12961:
12837:
12734:
12718:
12695:
12472:
12206:
12189:
12149:
12060:
11955:
11917:
11888:
11848:
11808:
11754:
11671:
11357:
11352:
11120:
Signal design for good correlation: for wireless communication, cryptography, and radar
10948:
10825:
10792:
10645:
10619:
10397:
10392:
10224:
10168:
10144:
10093:
10020:
10005:
9655:
lags of the residuals, where 'k' is the order of the test. The simplest version of the
9552:
9532:
9365:
9347:
8930:
7740:
7714:{\displaystyle R(j,k,\ell )=\sum _{n,q,r}x_{n,q,r}\,{\overline {x}}_{n-j,q-k,r-\ell }.}
7346:
7292:
7125:
7048:
7027:
6599:
6484:
6464:
6140:
6120:
6114:
5733:
5705:
2959:
603:
583:
498:
427:
407:
9891:
to provide quantitative insight into molecular-level diffusion and chemical reactions.
6547:
2112:
13446:
13357:
13327:
13319:
13139:
13130:
13055:
12986:
12842:
12827:
12802:
12690:
12631:
12497:
12485:
12111:
12028:
11972:
11895:
11739:
11661:
11440:
11314:
11147:
11144:
11132:
11068:
11044:
10952:
10910:
10887:
10879:
10830:
10771:
10701:
10668:
10589:
10564:
10539:
10514:
10472:
10441:
10351:
10042:
9941:
8875:
7283:
7253:
5670:
5392:
5305:
3072:
317:
202:
197:
65:
9675:. Under the null hypothesis of no autocorrelation, this statistic is asymptotically
8648:, several efficient algorithms exist which can compute the autocorrelation in order
13382:
13337:
13101:
13088:
12981:
12956:
12890:
12822:
12700:
12308:
12201:
12134:
12047:
11994:
11813:
11684:
11478:
11362:
11277:
11244:
11103:
10940:
10869:
10820:
10812:
10734:
10730:
10649:
10637:
10000:, autocorrelation (when applied at time scales smaller than a second) is used as a
9902:
9895:
9307:
9246:
7143:
4728:
4724:
3039:
2145:
16:
Correlation of a signal with a time-shifted copy of itself, as a function of shift
13299:
12905:
12832:
12507:
12381:
12354:
12331:
12300:
11927:
11922:
11876:
11606:
11257:
11062:
10972:
10138:
10111:
10078:
data, autocorrelation must be taken into account for correct error determination.
9964:
9929:
9636:
overestimated) when the autocorrelations of the errors at low lags are positive.
8924:
7732:
7577:
6161:
457:
301:
297:
12789:
10056:, autocorrelation is used to study and characterize the spatial distribution of
9585:, autocorrelation in a variable of interest is typically modeled either with an
13248:
13243:
11706:
11636:
11282:
11083:
10944:
10330:
10185:. A series is serially independent if there is no dependence between any pair.
10104:
9945:
9656:
8640:
8632:
The procedure can be regarded as an application of the convolution property of
3787:
3783:
827:
362:
328:
10816:
10641:
7735:
sequence, it is frequently necessary to compute the autocorrelation with high
13491:
13405:
13372:
13235:
13196:
13007:
12976:
12440:
12394:
11999:
11701:
11528:
11292:
11287:
11107:
11058:
10883:
10114:, autocorrelation has been used to accurately measure power system frequency.
10038:
9950:
6955:
3711:
3584:
2385:
1767:
The definition of the autocorrelation coefficient of a stochastic process is
1339:
449:
285:
9639:
The traditional test for the presence of first-order autocorrelation is the
796:{\displaystyle \operatorname {R} _{XX}(t_{1},t_{2})=\operatorname {E} \left}
13347:
13280:
13257:
13172:
12502:
11798:
11696:
11631:
11573:
11558:
11495:
11450:
10891:
10834:
10061:
10053:
10009:
9633:
9617:
835:
5893:{\displaystyle R_{yy}(\ell )=\sum _{n\in Z}y(n)\,{\overline {y(n-\ell )}}}
1193:
13390:
13352:
13035:
12936:
12798:
12611:
12578:
12070:
11987:
11982:
11626:
11583:
11563:
11543:
11533:
11302:
10993:"A New Method for Fast Frequency Measurement for Protection Applications"
10346:
10134:
10082:
9315:
8633:
7310:
2923:
453:
321:
289:
190:
4917:
All eigenvalues of the autocorrelation matrix are real and non-negative.
12236:
11716:
11416:
11347:
11297:
11272:
11192:
11115:
11028:
10874:
10849:
10086:
10068:
9974:
In optics, normalized autocorrelations and cross-correlations give the
9717:
358:
23:
10438:
Probability and Random
Processes for Electrical and Computer Engineers
10107:
can affect the optimal portion of the portfolio to hold in that asset.
9944:, or time shift, between the point of time at the transmission of the
9643:
or, if the explanatory variables include a lagged dependent variable,
8885:
correlation can be performed by using brute force calculation for low
6951:, which is easy to prove from the definition. In the continuous case,
1481:{\displaystyle \operatorname {R} _{XX}(\tau )=\operatorname {E} \left}
12389:
12241:
11861:
11656:
11568:
11553:
11548:
11513:
11152:
9986:
9982:
8901:
7569:
4566:{\displaystyle \mathbf {X} =\left(X_{1},X_{2},X_{3}\right)^{\rm {T}}}
3908:
1187:
334:
11084:"Computational Design of Sequences with Good Correlation Properties"
9364:. This estimate is always biased; however, it usually has a smaller
9015:, an estimate of the autocorrelation coefficient may be obtained as
11905:
11523:
11400:
11395:
11390:
9251:
3791:
1760:) to normalize the autocovariance function to get a time-dependent
546:
313:
10624:
9928:
suspended in a fluid. A laser shining into the mixture produces a
9371:
Other possibilities derive from treating the two portions of data
2144:, with 1 indicating perfect correlation and â1 indicating perfect
38:
13410:
13111:
10060:
in the universe and in multi-wavelength observations of low mass
10046:
10034:
9925:
7279:) is the sum of the autocorrelations of each function separately.
445:
7553:{\displaystyle R_{ff}(\tau )=(f*g_{-1}({\overline {f}}))(\tau )}
13332:
12313:
12287:
12267:
11518:
11309:
10057:
9990:
7822:{\displaystyle R_{xx}(j)=\sum _{n}x_{n}\,{\overline {x}}_{n-j}}
1756:
It is common practice in some disciplines (e.g. statistics and
10793:"Fluorescence Correlation Spectroscopy: Past, Present, Future"
9254:
of the process are not known there are several possibilities:
3583:(also called second moment) of a (potentially time-dependent)
125:
11161:
10356:
10013:
9997:
9906:
9899:
9894:
Another application of autocorrelation is the measurement of
9628:). While it does not bias the OLS coefficient estimates, the
4600:{\displaystyle \operatorname {R} _{\mathbf {X} \mathbf {X} }}
185:
Above: A plot of a series of 100 random numbers concealing a
90:
10929:
10848:
HoĆyst, Robert; Poniewierski, Andrzej; Zhang, Xuzhu (2017).
5315:
3775:{\displaystyle \mathbf {X} =(X_{1},\ldots ,X_{n})^{\rm {T}}}
3648:{\displaystyle \mathbf {X} =(X_{1},\ldots ,X_{n})^{\rm {T}}}
11252:
10103:, the presence or absence of autocorrelation in an asset's
9880:
9625:
6884:
A fundamental property of the autocorrelation is symmetry,
5299:
4717:
516:
186:
8927:
process with known mean and variance for which we observe
5725:
352:
181:
10511:
Measurement and Data
Analysis for Engineering and Science
10096:
imaging, autocorrelation is used to visualize blood flow.
9937:
9569:'s, the variance calculated may turn out to be negative.
11142:
10687:
9879:
Autocorrelation's ability to find repeating patterns in
8904:
density to compute higher values, resulting in the same
10847:
10563:(3rd ed.). Upper Saddle River, NJ: PrenticeâHall.
9518:{\displaystyle \{X_{k+1},\,X_{k+2},\,\ldots ,\,X_{n}\}}
8663:
allows computing the autocorrelation from the raw data
7286:, it maintains all the properties of cross-correlation.
1742:{\displaystyle \operatorname {K} _{XX}(0)=\sigma ^{2}.}
1194:
Definition for wide-sense stationary stochastic process
10559:
Box, G. E. P.; Jenkins, G. M.; Reinsel, G. C. (1994).
10494:
Probability, Random variables and
Stochastic processes
10004:
for both instrument tuners and "Auto Tune" (used as a
8602:{\displaystyle R_{xx}=(\ldots ,14,1,1,14,1,1,\ldots )}
7572:
autocorrelation is defined similarly. For example, in
3974:
841:
Subtracting the mean before multiplication yields the
349:
are specific forms of processes with autocorrelation.
10279:
10233:
10194:
10171:
10147:
9851:
9816:
9772:
9737:
9720:(Heteroskedasticity and Autocorrelation Consistent).
9683:
9555:
9535:
9451:
9438:{\displaystyle \{X_{1},\,X_{2},\,\ldots ,\,X_{n-k}\}}
9377:
9350:
9324:
9284:
9264:
9223:
9203:
9177:
9023:
8953:
8933:
8686:
8615:
8531:
8444:
8364:
8288:
8241:
8169:
7993:
7956:
7882:
7835:
7749:
7588:
7474:
7435:
7369:
7349:
7319:
7295:
7265:
7177:
7157:
7128:
7056:
7030:
6963:
6890:
6751:
6624:
6602:
6550:
6530:
6507:
6487:
6467:
6172:
6143:
6123:
5916:
5808:
5776:
5756:
5736:
5708:
5679:
5637:
5453:
5430:
5401:
5358:
5329:
5116:
4930:
4832:
4744:
4671:
4639:
4613:
4579:
4499:
4464:
4388:
4360:
3948:
3917:
3885:
3807:
3719:
3687:
3661:
3592:
3455:
3334:
3202:
3083:
3047:
3014:
2982:
2962:
2936:
2739:
2685:
2605:
2513:
2394:
2360:
2163:
2115:
2085:
1775:
1697:
1504:
1400:
1348:
1317:
1290:
1263:
1243:
1204:
908:
878:
851:
812:
687:
657:
630:
606:
586:
554:
524:
501:
466:
430:
410:
375:
320:
for analyzing functions or series of values, such as
253:
227:
13074:
Autoregressive conditional heteroskedasticity (ARCH)
7563:
4924:
is related to the autocorrelation matrix as follows:
3574:
10019:Autocorrelation in space rather than time, via the
9008:{\displaystyle \{X_{1},\,X_{2},\,\ldots ,\,X_{n}\}}
8521:then we get a circular autocorrelation (similar to
4380:, the autocorrelation matrix is instead defined by
3326:can be re-expressed in terms of real cosines only:
12536:
11032:
10768:An Introduction to Modern Econometrics Using Stata
10297:
10265:
10215:
10177:
10153:
9863:
9837:
9802:
9758:
9696:
9561:
9541:
9517:
9437:
9356:
9336:
9297:
9270:
9236:
9209:
9189:
9161:
9007:
8939:
8860:
8624:
8601:
8514:{\displaystyle x=(\ldots ,2,3,-1,2,3,-1,\ldots ),}
8513:
8429:
8350:
8275:
8227:
8153:
7975:
7942:
7868:
7821:
7713:
7552:
7460:
7421:
7355:
7335:
7301:
7271:
7237:
7163:
7134:
7114:
7036:
7016:
6943:
6860:
6733:
6608:
6588:
6536:
6516:
6493:
6473:
6456:
6432:
6149:
6129:
6103:
5892:
5791:
5762:
5742:
5714:
5694:
5661:
5620:
5436:
5416:
5383:
5344:
5288:
5102:
4906:
4818:
4706:
4657:
4625:
4599:
4565:
4478:
4448:
4368:
4344:
3929:
3899:
3868:
3774:
3695:
3673:
3647:
3564:
3440:
3312:
3187:
3063:
3030:
2988:
2968:
2948:
2907:
2713:
2671:
2584:
2499:
2376:
2326:
2136:
2101:
2069:
1741:
1678:
1480:
1380:
1330:
1303:
1276:
1249:
1225:
1174:
891:
864:
818:
795:
670:
643:
612:
592:
572:
537:
507:
479:
436:
416:
396:
265:
239:
11081:
11039:(Second ed.). New York: Macmillan. pp.
10558:
10041:makes use of autocorrelation in conjunction with
9920:data, which notably enables determination of the
9601:(ARIMA). With multiple interrelated data series,
8609:which has the same period as the signal sequence
2926:signal will have a strong peak (represented by a
2917:
2109:is well defined, its value must lie in the range
189:function. Below: The sine function revealed in a
13489:
10141:has serial dependence if the value at some time
9597:(ARMA), or an extension of the latter called an
8915:efficiency, but with lower memory requirements.
7115:{\displaystyle R_{ff}(-\tau )=R_{ff}^{*}(\tau )}
6331:
6207:
3703:. The autocorrelation matrix is used in various
12622:Multivariate adaptive regression splines (MARS)
10536:Communication Systems Engineering (2nd Edition)
10338:(transformation for autocorrelated error terms)
10227:, then statistical dependence between the pair
10688:Percival, Donald B.; Andrew T. Walden (1993).
10608:
9599:autoregressive integrated moving average model
8163:Thus the required autocorrelation sequence is
11177:
11057:
10909:(Third ed.). CRC Press. pp. 18â19.
10584:Frenkel, D.; Smit, B. (2002). "chap. 4.4.2".
10561:Time Series Analysis: Forecasting and Control
9712:Responses to nonzero autocorrelation include
7343:is a function which manipulates the function
7249:. The same result holds in the discrete case.
7238:{\displaystyle |R_{ff}(\tau )|\leq R_{ff}(0)}
6544:is replaced by integration over any interval
1388:. This gives the more familiar forms for the
162:
11082:Soltanalian, Mojtaba; Stoica, Petre (2012).
9887:Autocorrelation analysis is used heavily in
9512:
9452:
9432:
9378:
9002:
8954:
7282:Since autocorrelation is a specific type of
7017:{\displaystyle R_{ff}(-\tau )=R_{ff}(\tau )}
6944:{\displaystyle R_{ff}(\tau )=R_{ff}(-\tau )}
6481:is a continuous periodic function of period
2724:
10583:
10467:
10465:
10463:
10461:
10459:
10457:
9898:and the measurement of very-short-duration
8889:values, and then progressively binning the
4826:for a real random vector, and respectively
2354:The fact that the autocorrelation function
361:, the autocorrelation of a real or complex
11222:
11184:
11170:
11131:(Second ed.). Elsevier. pp. 108â112
10904:
10488:
10486:
10484:
7743:based on the signal processing definition
7256:is, itself, periodic with the same period.
2999:
2714:{\displaystyle \operatorname {R} _{XX}(0)}
169:
155:
11835:
10990:
10968:"Auto-Tune: Why Pop Music Sounds Perfect"
10965:
10873:
10824:
10662:
10623:
10403:Unbiased estimation of standard deviation
10030:when sampling a heterogeneous population.
9501:
9494:
9474:
9415:
9408:
9394:
8991:
8984:
8970:
7795:
7660:
7576:the autocorrelation of a square-summable
6851:
6724:
6395:
6286:
6061:
5862:
5607:
5536:
5316:Autocorrelation of continuous-time signal
4894:
4806:
3548:
3427:
3296:
3174:
2922:The autocorrelation of a continuous-time
209:. For the operations involving function
10720:
10588:(2nd ed.). London: Academic Press.
10454:
10431:
10429:
10427:
10425:
10423:
10421:
10419:
8430:{\displaystyle R_{xx}(-2)=R_{xx}(2)=-2,}
7943:{\displaystyle x_{0}=2,x_{1}=3,x_{2}=-1}
7726:
5391:is most often defined as the continuous
5300:Autocorrelation of deterministic signals
5110:Respectively for complex random vectors:
4718:Properties of the autocorrelation matrix
196:
180:
10998:. Schweitzer Engineering Laboratories.
10696:. Cambridge University Press. pp.
10533:
10481:
8351:{\displaystyle R_{xx}(-1)=R_{xx}(1)=3,}
5726:Autocorrelation of discrete-time signal
3031:{\displaystyle \operatorname {R} _{XX}}
2733:, inequality for stochastic processes:
2377:{\displaystyle \operatorname {R} _{XX}}
834:. Note that the expectation may not be
353:Autocorrelation of stochastic processes
13490:
13148:KaplanâMeier estimator (product limit)
11088:IEEE Transactions on Signal Processing
11027:
10504:
10502:
10435:
9949:along in order to accommodate for the
9572:
5908:, the autocorrelations are defined as
5906:wide-sense-stationary random processes
13221:
12788:
12535:
11834:
11604:
11221:
11165:
11143:
10790:
10416:
10362:Fluorescence correlation spectroscopy
9889:fluorescence correlation spectroscopy
9883:yields many applications, including:
8228:{\displaystyle R_{xx}=(-2,3,14,3,-2)}
3008:relates the autocorrelation function
13458:
13158:Accelerated failure time (AFT) model
10765:
10667:. London, New York: Academic Press.
10538:(2 ed.). Pearson. p. 168.
10508:
10216:{\displaystyle \left\{X_{t}\right\}}
10118:
9985:, autocorrelation can determine the
2349:
1226:{\displaystyle \left\{X_{t}\right\}}
397:{\displaystyle \left\{X_{t}\right\}}
13470:
12753:Analysis of variance (ANOVA, anova)
11605:
11122:. Cambridge University Press, 2005.
10499:
9916:Autocorrelation is used to analyze
9803:{\displaystyle \tau =0,1,\ldots ,q}
9632:tend to be underestimated (and the
9595:autoregressive-moving-average model
8639:While the brute force algorithm is
4914:in case of a complex random vector.
13:
12848:CochranâMantelâHaenszel statistics
11474:Pearson product-moment correlation
11021:
10791:Elson, Elliot L. (December 2011).
10586:Understanding Molecular Simulation
9659:from this auxiliary regression is
9605:(VAR) or its extensions are used.
7422:{\displaystyle g_{-1}(f)(t)=f(-t)}
6531:
6511:
6341:
6289:
6217:
6117:, these will also be functions of
6038:
5950:
5662:{\displaystyle {\overline {f(t)}}}
5610:
5563:
5558:
5539:
5492:
5487:
5280:
5260:
5243:
5224:
5211:
5188:
5157:
5137:
5118:
5094:
5074:
5057:
5038:
5025:
5002:
4971:
4951:
4932:
4848:
4841:
4760:
4753:
4707:{\displaystyle \operatorname {E} }
4672:
4581:
4557:
4470:
4434:
4412:
4390:
4299:
4260:
4226:
4162:
4123:
4089:
4050:
4011:
3977:
3950:
3891:
3855:
3831:
3809:
3766:
3639:
3551:
3500:
3494:
3489:
3430:
3376:
3371:
3336:
3299:
3247:
3241:
3236:
3177:
3125:
3120:
3085:
3016:
2855:
2805:
2747:
2687:
2645:
2612:
2594:
2546:
2515:
2447:
2396:
2362:
2236:
2193:
1914:
1825:
1699:
1611:
1533:
1506:
1429:
1402:
1071:
957:
910:
819:{\displaystyle \operatorname {E} }
813:
736:
689:
201:Visual comparison of convolution,
14:
13519:
10933:Superlattices and Microstructures
10665:Spectral Analysis and Time Series
10534:Proakis, John (August 31, 2001).
7564:Multi-dimensional autocorrelation
5352:, the continuous autocorrelation
4727:for complex random vectors and a
3579:The (potentially time-dependent)
3575:Autocorrelation of random vectors
2155:(WSS) process, the definition is
1381:{\displaystyle \tau =t_{2}-t_{1}}
316:frequencies. It is often used in
13469:
13457:
13445:
13432:
13431:
13222:
10991:Kasztenny, Bogdan (March 2016).
10372:Partial autocorrelation function
10321:Autocorrelation of a formal word
9924:of nanometer-sized particles or
5270:
5253:
5234:
5229:
5198:
5181:
5167:
5150:
5128:
5123:
5084:
5067:
5048:
5043:
5012:
4995:
4981:
4964:
4942:
4937:
4885:
4868:
4858:
4853:
4835:
4797:
4780:
4770:
4765:
4747:
4734:The autocorrelation matrix is a
4723:The autocorrelation matrix is a
4591:
4586:
4501:
4428:
4422:
4400:
4395:
4362:
3960:
3955:
3849:
3843:
3819:
3814:
3721:
3689:
3594:
2507:respectively for a WSS process:
1751:
830:operator and the bar represents
37:
13107:Least-squares spectral analysis
11005:from the original on 2022-10-09
10984:
10959:
10923:
10898:
10841:
10784:
10759:
10749:"Serial correlation techniques"
10741:
10714:
10681:
9874:
8870:where IFFT denotes the inverse
7245:. This is a consequence of the
6878:wide-sense stationary processes
6870:
6457:Definition for periodic signals
4878:
4790:
1762:Pearson correlation coefficient
573:{\displaystyle \sigma _{t}^{2}}
515:. Suppose that the process has
273:are identical in this example.
12088:Mean-unbiased minimum-variance
11191:
11064:A Guide to Modern Econometrics
10966:Tyrangiel, Josh (2009-02-05).
10735:10.1080/00031305.1993.10475997
10656:
10602:
10577:
10552:
10527:
10440:. Cambridge University Press.
10260:
10234:
10101:intertemporal portfolio choice
9826:
9820:
9759:{\displaystyle R(\tau )\neq 0}
9747:
9741:
9593:(MA), their combination as an
9156:
9131:
9128:
9109:
9066:
9054:
9042:
9036:
9030:
8851:
8848:
8842:
8836:
8820:
8814:
8804:
8798:
8780:
8774:
8754:
8748:
8738:
8735:
8729:
8723:
8707:
8701:
8596:
8548:
8505:
8451:
8412:
8406:
8387:
8378:
8336:
8330:
8311:
8302:
8261:
8255:
8222:
8186:
7863:
7842:
7769:
7763:
7610:
7592:
7547:
7541:
7538:
7535:
7522:
7500:
7494:
7488:
7455:
7449:
7416:
7407:
7398:
7392:
7389:
7383:
7232:
7226:
7206:
7202:
7196:
7179:
7109:
7103:
7079:
7070:
7011:
7005:
6986:
6977:
6938:
6929:
6910:
6904:
6842:
6830:
6821:
6815:
6771:
6765:
6715:
6709:
6700:
6688:
6644:
6638:
6583:
6551:
6414:
6402:
6392:
6386:
6338:
6320:
6314:
6277:
6271:
6262:
6250:
6214:
6196:
6190:
6080:
6068:
6058:
6052:
6028:
6022:
5991:
5979:
5970:
5964:
5940:
5934:
5881:
5869:
5859:
5853:
5828:
5822:
5786:
5780:
5689:
5683:
5650:
5644:
5598:
5586:
5577:
5571:
5527:
5521:
5512:
5500:
5473:
5467:
5411:
5405:
5378:
5372:
5339:
5333:
5275:
5266:
5257:
5249:
5217:
5206:
5202:
5194:
5177:
5174:
5171:
5163:
5146:
5143:
5089:
5080:
5071:
5063:
5031:
5020:
5016:
5008:
4991:
4988:
4985:
4977:
4960:
4957:
4701:
4678:
4652:
4640:
4440:
4418:
4328:
4305:
4289:
4266:
4255:
4232:
4191:
4168:
4152:
4129:
4118:
4095:
4079:
4056:
4040:
4017:
4006:
3983:
3761:
3728:
3634:
3601:
3545:
3530:
3521:
3515:
3475:
3469:
3424:
3409:
3400:
3394:
3357:
3351:
3268:
3262:
3222:
3216:
3149:
3143:
3106:
3100:
2918:Autocorrelation of white noise
2890:
2867:
2840:
2817:
2788:
2762:
2708:
2702:
2666:
2660:
2633:
2627:
2570:
2561:
2536:
2530:
2488:
2462:
2437:
2411:
2297:
2278:
2272:
2247:
2214:
2208:
2183:
2177:
2131:
2116:
2011:
1971:
1965:
1925:
1866:
1840:
1815:
1789:
1720:
1714:
1594:
1575:
1569:
1544:
1527:
1521:
1423:
1417:
1054:
1014:
1008:
968:
951:
925:
730:
704:
1:
13401:Geographic information system
12617:Simultaneous equations models
10766:Baum, Christopher F. (2006).
10409:
10266:{\displaystyle (X_{t},X_{s})}
10165:on the value at another time
8918:
8438:happens to be periodic, i.e.
8276:{\displaystyle R_{xx}(0)=14,}
7461:{\displaystyle R_{ff}(\tau )}
5730:The discrete autocorrelation
5384:{\displaystyle R_{ff}(\tau )}
2344:
1235:wide-sense stationary process
620:. Then the definition of the
310:missing fundamental frequency
213:, and assuming the height of
12584:Coefficient of determination
12195:Uniformly most powerful test
10388:PraisâWinsten transformation
10377:Phylogenetic autocorrelation
9978:of an electromagnetic field.
9958:small-angle X-ray scattering
9673:coefficient of determination
9244:are known, this estimate is
7802:
7667:
7530:
6846:
6719:
6451:short-time Fourier transform
6445:Alternatively, signals that
6418:
6281:
6160:For processes that are also
6084:
5995:
5885:
5654:
5602:
5531:
5312:or autocovariance function.
4736:positive semidefinite matrix
4479:{\displaystyle {}^{\rm {H}}}
4369:{\displaystyle \mathbf {Z} }
3900:{\displaystyle {}^{\rm {T}}}
3696:{\displaystyle \mathbf {X} }
2574:
2492:
2301:
2015:
1671:
1644:
1598:
1462:
1154:
1105:
1058:
770:
193:produced by autocorrelation.
7:
13153:Proportional hazards models
13097:Spectral density estimation
13079:Vector autoregression (VAR)
12513:Maximum posterior estimator
11745:Randomized controlled trial
10308:
10012:, for example to determine
9922:particle size distributions
9298:{\displaystyle \sigma ^{2}}
9237:{\displaystyle \sigma ^{2}}
6113:For processes that are not
5770:for a discrete-time signal
5310:autocorrelation coefficient
1277:{\displaystyle \sigma ^{2}}
312:in a signal implied by its
10:
13524:
12913:Multivariate distributions
11333:Average absolute deviation
10945:10.1016/j.spmi.2019.106173
10336:CochraneâOrcutt estimation
10128:Correlation and dependence
9940:system to correct for the
9864:{\displaystyle \tau >q}
9838:{\displaystyle R(\tau )=0}
9344:in the above formula with
8881:Alternatively, a multiple
7869:{\displaystyle x=(2,3,-1)}
6954:the autocorrelation is an
5702:. Note that the parameter
2102:{\displaystyle \rho _{XX}}
339:trend-stationary processes
131:Cross-correlation function
96:Cross-correlation function
31:Correlation and covariance
13427:
13381:
13318:
13271:
13234:
13230:
13217:
13189:
13171:
13138:
13129:
13087:
13034:
12995:
12944:
12935:
12901:Structural equation model
12856:
12813:
12809:
12784:
12743:
12709:
12663:
12630:
12592:
12559:
12555:
12531:
12471:
12380:
12299:
12263:
12254:
12237:Score/Lagrange multiplier
12222:
12175:
12120:
12046:
12037:
11847:
11843:
11830:
11789:
11763:
11715:
11670:
11652:Sample size determination
11617:
11613:
11600:
11504:
11459:
11433:
11415:
11371:
11323:
11243:
11234:
11230:
11217:
11199:
10817:10.1016/j.bpj.2011.11.012
10723:The American Statistician
10663:Priestley, M. B. (1982).
10642:10.1016/j.cpc.2011.01.009
10513:. New York: McGrawâHill.
10509:Dunn, Patrick F. (2005).
10383:Pitch detection algorithm
10326:Autocorrelation technique
10298:{\displaystyle \tau =s-t}
10002:pitch detection algorithm
9969:scanning probe microscopy
9714:generalized least squares
9697:{\displaystyle \chi ^{2}}
9318:-based estimate replaces
9171:for any positive integer
7252:The autocorrelation of a
7047:the autocorrelation is a
4626:{\displaystyle 3\times 3}
4573:is a random vector, then
3930:{\displaystyle n\times n}
3705:digital signal processing
3674:{\displaystyle n\times n}
2731:CauchyâSchwarz inequality
2725:CauchyâSchwarz inequality
1689:In particular, note that
404:be a random process, and
141:Cross-covariance function
119:For deterministic signals
106:Cross-covariance function
13396:Environmental statistics
12918:Elliptical distributions
12711:Generalized linear model
12640:Simple linear regression
12410:HodgesâLehmann estimator
11867:Probability distribution
11776:Stochastic approximation
11338:Coefficient of variation
11108:10.1109/TSP.2012.2186134
11035:Elements of Econometrics
10905:Van Sickle, Jan (2008).
10436:Gubner, John A. (2006).
10076:Markov chain Monte Carlo
10037:algorithm for analyzing
10028:mean value uncertainties
9918:dynamic light scattering
9718:NeweyâWest HAC estimator
7983:for all other values of
7737:computational efficiency
7731:For data expressed as a
7247:rearrangement inequality
6517:{\displaystyle -\infty }
6453:for a related process.)
4731:for real random vectors.
3940:Written component-wise:
1493:auto-covariance function
1390:autocorrelation function
843:auto-covariance function
622:autocorrelation function
538:{\displaystyle \mu _{t}}
347:moving average processes
343:autoregressive processes
266:{\displaystyle f\star g}
126:Autocorrelation function
91:Autocorrelation function
84:For stochastic processes
61:Cross-correlation matrix
13056:Cross-correlation (XCF)
12664:Non-standard predictors
12098:LehmannâScheffĂ© theorem
11771:Adaptive clinical trial
11125:Klapetek, Petr (2018).
11114:Solomon W. Golomb, and
10367:Optical autocorrelation
10163:statistically dependent
9911:optical autocorrelators
9723:In the estimation of a
9667:is the sample size and
9641:DurbinâWatson statistic
9250:. If the true mean and
8874:. The asterisk denotes
8676:fast Fourier transforms
8661:WienerâKhinchin theorem
7976:{\displaystyle x_{i}=0}
7044:is a real function, and
6743:which is equivalent to
6537:{\displaystyle \infty }
6501:, the integration from
3324:WienerâKhinchin theorem
3006:WienerâKhinchin theorem
3000:WienerâKhinchin theorem
2949:{\displaystyle \tau =0}
495:of the process at time
136:Autocovariance function
101:Autocovariance function
71:Cross-covariance matrix
13452:Mathematics portal
13273:Engineering statistics
13181:NelsonâAalen estimator
12758:Analysis of covariance
12645:Ordinary least squares
12569:Pearson product-moment
11973:Statistical functional
11884:Empirical distribution
11717:Controlled experiments
11446:Frequency distribution
11224:Descriptive statistics
10907:GPS for Land Surveyors
10492:Papoulis, Athanasius,
10316:Autocorrelation matrix
10299:
10267:
10217:
10179:
10155:
9865:
9839:
9804:
9760:
9698:
9610:ordinary least squares
9563:
9543:
9519:
9439:
9358:
9338:
9299:
9272:
9238:
9211:
9191:
9190:{\displaystyle k<n}
9163:
9108:
9009:
8941:
8872:fast Fourier transform
8862:
8636:of a discrete signal.
8626:
8603:
8515:
8431:
8352:
8277:
8229:
8155:
7977:
7944:
7870:
7823:
7715:
7554:
7462:
7423:
7357:
7337:
7336:{\displaystyle g_{-1}}
7303:
7273:
7239:
7165:
7136:
7116:
7038:
7018:
6945:
6862:
6735:
6610:
6590:
6538:
6518:
6495:
6475:
6434:
6382:
6151:
6131:
6105:
5894:
5793:
5764:
5744:
5716:
5696:
5663:
5622:
5438:
5418:
5385:
5346:
5290:
5104:
4922:auto-covariance matrix
4908:
4820:
4708:
4659:
4627:
4601:
4567:
4480:
4450:
4370:
4346:
3931:
3901:
3870:
3796:autocorrelation matrix
3776:
3697:
3675:
3649:
3581:autocorrelation matrix
3566:
3442:
3314:
3189:
3065:
3064:{\displaystyle S_{XX}}
3040:power spectral density
3032:
2990:
2970:
2950:
2909:
2715:
2673:
2586:
2501:
2378:
2339:statistical dependence
2328:
2138:
2103:
2071:
1743:
1680:
1482:
1382:
1332:
1305:
1278:
1251:
1227:
1176:
893:
866:
820:
797:
672:
645:
614:
594:
574:
539:
509:
491:) produced by a given
481:
438:
424:be any point in time (
418:
398:
274:
267:
241:
194:
66:Auto-covariance matrix
56:Autocorrelation matrix
13368:Population statistics
13310:System identification
13044:Autocorrelation (ACF)
12972:Exponential smoothing
12886:Discriminant analysis
12881:Canonical correlation
12745:Partition of variance
12607:Regression validation
12451:(JonckheereâTerpstra)
12350:Likelihood-ratio test
12039:Frequentist inference
11951:Locationâscale family
11872:Sampling distribution
11837:Statistical inference
11804:Cross-sectional study
11791:Observational studies
11750:Randomized experiment
11579:Stem-and-leaf display
11381:Central limit theorem
10980:on February 10, 2009.
10612:Comput. Phys. Commun.
10300:
10268:
10218:
10180:
10156:
9866:
9840:
9805:
9761:
9699:
9603:vector autoregression
9564:
9544:
9520:
9440:
9359:
9339:
9300:
9273:
9239:
9212:
9197:. When the true mean
9192:
9164:
9082:
9010:
8942:
8863:
8627:
8604:
8516:
8432:
8353:
8278:
8230:
8156:
7978:
7945:
7871:
7824:
7727:Efficient computation
7716:
7555:
7463:
7429:, the definition for
7424:
7358:
7338:
7304:
7274:
7272:{\displaystyle \tau }
7240:
7166:
7164:{\displaystyle \tau }
7137:
7117:
7039:
7019:
6946:
6863:
6736:
6611:
6591:
6539:
6519:
6496:
6476:
6435:
6356:
6152:
6132:
6106:
5895:
5794:
5765:
5763:{\displaystyle \ell }
5745:
5717:
5697:
5664:
5623:
5439:
5437:{\displaystyle \tau }
5419:
5386:
5347:
5291:
5105:
4909:
4821:
4709:
4660:
4658:{\displaystyle (i,j)}
4628:
4602:
4568:
4481:
4451:
4378:complex random vector
4371:
4347:
3932:
3911:matrix of dimensions
3902:
3871:
3777:
3698:
3676:
3650:
3567:
3443:
3315:
3190:
3066:
3033:
2991:
2989:{\displaystyle \tau }
2971:
2951:
2910:
2716:
2674:
2587:
2502:
2379:
2329:
2153:wide-sense stationary
2139:
2104:
2072:
1744:
1681:
1483:
1383:
1333:
1331:{\displaystyle t_{2}}
1306:
1304:{\displaystyle t_{1}}
1279:
1252:
1228:
1177:
894:
892:{\displaystyle t_{2}}
867:
865:{\displaystyle t_{1}}
821:
798:
673:
671:{\displaystyle t_{2}}
646:
644:{\displaystyle t_{1}}
615:
595:
575:
540:
510:
482:
480:{\displaystyle X_{t}}
439:
419:
399:
308:, or identifying the
280:, sometimes known as
268:
242:
200:
184:
13508:Time domain analysis
13291:Probabilistic design
12876:Principal components
12719:Exponential families
12671:Nonlinear regression
12650:General linear model
12612:Mixed effects models
12602:Errors and residuals
12579:Confounding variable
12481:Bayesian probability
12459:Van der Waerden test
12449:Ordered alternative
12214:Multiple comparisons
12093:RaoâBlackwellization
12056:Estimating equations
12012:Statistical distance
11730:Factorial experiment
11263:Arithmetic-Geometric
10342:Correlation function
10277:
10231:
10192:
10169:
10145:
9849:
9814:
9770:
9735:
9725:moving average model
9709:degrees of freedom.
9681:
9649:BreuschâGodfrey test
9645:Durbin's h statistic
9622:Gauss Markov theorem
9614:regression residuals
9591:moving average model
9587:autoregressive model
9553:
9533:
9449:
9375:
9348:
9322:
9282:
9271:{\displaystyle \mu }
9262:
9221:
9210:{\displaystyle \mu }
9201:
9175:
9021:
8951:
8931:
8684:
8613:
8529:
8523:circular convolution
8442:
8362:
8286:
8239:
8167:
7991:
7954:
7880:
7833:
7747:
7586:
7472:
7433:
7367:
7347:
7317:
7293:
7289:By using the symbol
7263:
7175:
7155:
7126:
7054:
7028:
6961:
6888:
6749:
6622:
6600:
6548:
6528:
6505:
6485:
6465:
6170:
6141:
6121:
5914:
5806:
5792:{\displaystyle y(n)}
5774:
5754:
5734:
5706:
5695:{\displaystyle f(t)}
5677:
5635:
5451:
5428:
5424:with itself, at lag
5417:{\displaystyle f(t)}
5399:
5356:
5345:{\displaystyle f(t)}
5327:
5114:
4928:
4830:
4742:
4669:
4637:
4611:
4577:
4497:
4462:
4386:
4358:
3946:
3915:
3883:
3805:
3717:
3685:
3659:
3590:
3453:
3332:
3200:
3081:
3045:
3012:
2980:
2960:
2956:and will be exactly
2934:
2928:Dirac delta function
2737:
2683:
2603:
2511:
2392:
2358:
2161:
2113:
2083:
1773:
1758:time series analysis
1695:
1502:
1398:
1346:
1315:
1288:
1261:
1250:{\displaystyle \mu }
1241:
1202:
906:
876:
849:
810:
685:
655:
628:
604:
584:
552:
522:
499:
464:
428:
408:
373:
251:
225:
22:Part of a series on
13363:Official statistics
13286:Methods engineering
12967:Seasonal adjustment
12735:Poisson regressions
12655:Bayesian regression
12594:Regression analysis
12574:Partial correlation
12546:Regression analysis
12145:Prediction interval
12140:Likelihood interval
12130:Confidence interval
12122:Interval estimation
12083:Unbiased estimators
11901:Model specification
11781:Up-and-down designs
11469:Partial correlation
11425:Index of dispersion
11343:Interquartile range
11100:2012ITSP...60.2180S
10866:2017SMat...13.1267H
10809:2011BpJ...101.2855E
10797:Biophysical Journal
10634:2011CoPhC.182.1120C
10496:, McGraw-Hill, 1991
9976:degree of coherence
9579:regression analysis
9573:Regression analysis
9337:{\displaystyle n-k}
8797:
8659:. For example, the
7102:
6811:
6684:
6246:
5567:
5496:
4488:Hermitian transpose
3498:
3380:
3245:
3129:
2599:For a WSS process:
832:complex conjugation
569:
367:Pearson correlation
240:{\displaystyle g*f}
13383:Spatial statistics
13263:Medical statistics
13163:First hitting time
13117:Whittle likelihood
12768:Degrees of freedom
12763:Multivariate ANOVA
12696:Heteroscedasticity
12508:Bayesian estimator
12473:Bayesian inference
12322:KolmogorovâSmirnov
12207:Randomization test
12177:Testing hypotheses
12150:Tolerance interval
12061:Maximum likelihood
11956:Exponential family
11889:Density estimation
11849:Statistical theory
11809:Natural experiment
11755:Scientific control
11672:Survey methodology
11358:Standard deviation
11145:Weisstein, Eric W.
11061:(10 August 2017).
10875:10.1039/C6SM02643E
10398:Triple correlation
10393:Scaled correlation
10379:(Galton's problem)
10295:
10263:
10213:
10175:
10151:
10094:medical ultrasound
10021:Patterson function
9861:
9835:
9800:
9756:
9694:
9559:
9539:
9515:
9435:
9366:mean squared error
9354:
9334:
9295:
9268:
9234:
9207:
9187:
9159:
9005:
8937:
8858:
8856:
8783:
8625:{\displaystyle x.}
8622:
8599:
8511:
8427:
8348:
8273:
8225:
8151:
8149:
7973:
7940:
7866:
7819:
7784:
7741:brute force method
7711:
7637:
7550:
7468:may be written as:
7458:
7419:
7363:and is defined as
7353:
7333:
7299:
7269:
7235:
7161:
7132:
7112:
7085:
7049:Hermitian function
7034:
7014:
6941:
6858:
6777:
6731:
6650:
6606:
6586:
6534:
6514:
6491:
6471:
6430:
6428:
6345:
6232:
6221:
6147:
6127:
6101:
6099:
5890:
5849:
5789:
5760:
5740:
5712:
5692:
5659:
5618:
5550:
5479:
5434:
5414:
5381:
5342:
5286:
5100:
4904:
4816:
4704:
4655:
4623:
4597:
4563:
4476:
4446:
4366:
4342:
4336:
3927:
3897:
3866:
3772:
3693:
3671:
3645:
3562:
3481:
3438:
3363:
3310:
3228:
3185:
3112:
3061:
3028:
2986:
2966:
2946:
2905:
2711:
2669:
2582:
2497:
2374:
2324:
2134:
2099:
2067:
1739:
1676:
1478:
1378:
1328:
1301:
1274:
1247:
1223:
1172:
889:
862:
816:
793:
668:
641:
610:
590:
570:
555:
535:
505:
477:
434:
414:
394:
282:serial correlation
275:
263:
237:
195:
49:For random vectors
13503:Signal processing
13485:
13484:
13423:
13422:
13419:
13418:
13358:National accounts
13328:Actuarial science
13320:Social statistics
13213:
13212:
13209:
13208:
13205:
13204:
13140:Survival function
13125:
13124:
12987:Granger causality
12828:Contingency table
12803:Survival analysis
12780:
12779:
12776:
12775:
12632:Linear regression
12527:
12526:
12523:
12522:
12498:Credible interval
12467:
12466:
12250:
12249:
12066:Method of moments
11935:Parametric family
11896:Statistical model
11826:
11825:
11822:
11821:
11740:Random assignment
11662:Statistical power
11596:
11595:
11592:
11591:
11441:Contingency table
11411:
11410:
11278:Generalized/power
11148:"Autocorrelation"
11074:978-1-119-40110-0
11050:978-0-02-365070-3
10916:978-0-8493-9195-8
10803:(12): 2855â2870.
10777:978-1-59718-013-9
10753:Statistical Ideas
10707:978-0-521-43541-3
10520:978-0-07-282538-1
10477:978-3-319-68074-3
10447:978-0-521-86470-1
10352:Cross-correlation
10188:If a time series
10178:{\displaystyle s}
10161:in the series is
10154:{\displaystyle t}
10124:Serial dependence
10119:Serial dependence
10085:(specifically in
10043:cross-correlation
9942:propagation delay
9562:{\displaystyle X}
9542:{\displaystyle k}
9357:{\displaystyle n}
9080:
9033:
8940:{\displaystyle n}
8876:complex conjugate
7805:
7775:
7670:
7616:
7533:
7356:{\displaystyle f}
7302:{\displaystyle *}
7284:cross-correlation
7254:periodic function
7135:{\displaystyle f}
7037:{\displaystyle f}
6849:
6722:
6609:{\displaystyle T}
6494:{\displaystyle T}
6474:{\displaystyle f}
6421:
6354:
6330:
6284:
6230:
6206:
6150:{\displaystyle n}
6130:{\displaystyle t}
6087:
5998:
5888:
5834:
5743:{\displaystyle R}
5715:{\displaystyle t}
5671:complex conjugate
5657:
5605:
5534:
5393:cross-correlation
5306:signal processing
4882:
4794:
4411:
3830:
3073:Fourier transform
2969:{\displaystyle 0}
2577:
2495:
2388:can be stated as
2350:Symmetry property
2322:
2304:
2228:
2062:
2018:
1906:
1674:
1647:
1601:
1465:
1257:and the variance
1157:
1108:
1061:
773:
613:{\displaystyle t}
593:{\displaystyle t}
508:{\displaystyle t}
487:is the value (or
437:{\displaystyle t}
417:{\displaystyle t}
318:signal processing
203:cross-correlation
179:
178:
13515:
13473:
13472:
13461:
13460:
13450:
13449:
13435:
13434:
13338:Crime statistics
13232:
13231:
13219:
13218:
13136:
13135:
13102:Fourier analysis
13089:Frequency domain
13069:
13016:
12982:Structural break
12942:
12941:
12891:Cluster analysis
12838:Log-linear model
12811:
12810:
12786:
12785:
12727:
12701:Homoscedasticity
12557:
12556:
12533:
12532:
12452:
12444:
12436:
12435:(KruskalâWallis)
12420:
12405:
12360:Cross validation
12345:
12327:AndersonâDarling
12274:
12261:
12260:
12232:Likelihood-ratio
12224:Parametric tests
12202:Permutation test
12185:1- & 2-tails
12076:Minimum distance
12048:Point estimation
12044:
12043:
11995:Optimal decision
11946:
11845:
11844:
11832:
11831:
11814:Quasi-experiment
11764:Adaptive designs
11615:
11614:
11602:
11601:
11479:Rank correlation
11241:
11240:
11232:
11231:
11219:
11218:
11186:
11179:
11172:
11163:
11162:
11158:
11157:
11111:
11078:
11054:
11038:
11015:
11014:
11012:
11010:
11004:
10997:
10988:
10982:
10981:
10976:. Archived from
10963:
10957:
10956:
10927:
10921:
10920:
10902:
10896:
10895:
10877:
10860:(6): 1267â1275.
10845:
10839:
10838:
10828:
10788:
10782:
10781:
10763:
10757:
10756:
10745:
10739:
10738:
10718:
10712:
10711:
10695:
10685:
10679:
10678:
10660:
10654:
10653:
10627:
10618:(5): 1120â1129.
10606:
10600:
10599:
10581:
10575:
10574:
10556:
10550:
10549:
10531:
10525:
10524:
10506:
10497:
10490:
10479:
10469:
10452:
10451:
10433:
10304:
10302:
10301:
10296:
10272:
10270:
10269:
10264:
10259:
10258:
10246:
10245:
10222:
10220:
10219:
10214:
10212:
10208:
10207:
10184:
10182:
10181:
10176:
10160:
10158:
10157:
10152:
10112:numerical relays
9936:Utilized in the
9870:
9868:
9867:
9862:
9844:
9842:
9841:
9836:
9809:
9807:
9806:
9801:
9765:
9763:
9762:
9757:
9703:
9701:
9700:
9695:
9693:
9692:
9583:time series data
9568:
9566:
9565:
9560:
9548:
9546:
9545:
9540:
9524:
9522:
9521:
9516:
9511:
9510:
9490:
9489:
9470:
9469:
9444:
9442:
9441:
9436:
9431:
9430:
9404:
9403:
9390:
9389:
9363:
9361:
9360:
9355:
9343:
9341:
9340:
9335:
9304:
9302:
9301:
9296:
9294:
9293:
9277:
9275:
9274:
9269:
9243:
9241:
9240:
9235:
9233:
9232:
9216:
9214:
9213:
9208:
9196:
9194:
9193:
9188:
9168:
9166:
9165:
9160:
9149:
9148:
9121:
9120:
9107:
9096:
9081:
9079:
9078:
9077:
9049:
9035:
9034:
9026:
9014:
9012:
9011:
9006:
9001:
9000:
8980:
8979:
8966:
8965:
8946:
8944:
8943:
8938:
8914:
8899:
8888:
8884:
8867:
8865:
8864:
8859:
8857:
8796:
8791:
8773:
8772:
8700:
8699:
8673:
8658:
8647:
8631:
8629:
8628:
8623:
8608:
8606:
8605:
8600:
8544:
8543:
8520:
8518:
8517:
8512:
8436:
8434:
8433:
8428:
8405:
8404:
8377:
8376:
8357:
8355:
8354:
8349:
8329:
8328:
8301:
8300:
8282:
8280:
8279:
8274:
8254:
8253:
8234:
8232:
8231:
8226:
8182:
8181:
8160:
8158:
8157:
8152:
8150:
8116:
8095:
8094:
8068:
8067:
8043:
7997:
7986:
7982:
7980:
7979:
7974:
7966:
7965:
7949:
7947:
7946:
7941:
7930:
7929:
7911:
7910:
7892:
7891:
7875:
7873:
7872:
7867:
7828:
7826:
7825:
7820:
7818:
7817:
7806:
7798:
7794:
7793:
7783:
7762:
7761:
7720:
7718:
7717:
7712:
7707:
7706:
7671:
7663:
7659:
7658:
7636:
7574:three dimensions
7559:
7557:
7556:
7551:
7534:
7526:
7521:
7520:
7487:
7486:
7467:
7465:
7464:
7459:
7448:
7447:
7428:
7426:
7425:
7420:
7382:
7381:
7362:
7360:
7359:
7354:
7342:
7340:
7339:
7334:
7332:
7331:
7308:
7306:
7305:
7300:
7278:
7276:
7275:
7270:
7244:
7242:
7241:
7236:
7225:
7224:
7209:
7195:
7194:
7182:
7170:
7168:
7167:
7162:
7144:complex function
7141:
7139:
7138:
7133:
7121:
7119:
7118:
7113:
7101:
7096:
7069:
7068:
7043:
7041:
7040:
7035:
7023:
7021:
7020:
7015:
7004:
7003:
6976:
6975:
6950:
6948:
6947:
6942:
6928:
6927:
6903:
6902:
6867:
6865:
6864:
6859:
6850:
6845:
6825:
6810:
6803:
6802:
6792:
6791:
6790:
6764:
6763:
6740:
6738:
6737:
6732:
6723:
6718:
6704:
6683:
6676:
6675:
6665:
6664:
6663:
6637:
6636:
6615:
6613:
6612:
6607:
6595:
6593:
6592:
6589:{\displaystyle }
6587:
6576:
6575:
6563:
6562:
6543:
6541:
6540:
6535:
6523:
6521:
6520:
6515:
6500:
6498:
6497:
6492:
6480:
6478:
6477:
6472:
6439:
6437:
6436:
6431:
6429:
6422:
6417:
6397:
6381:
6370:
6355:
6347:
6344:
6313:
6312:
6293:
6292:
6285:
6280:
6266:
6245:
6240:
6231:
6223:
6220:
6189:
6188:
6156:
6154:
6153:
6148:
6136:
6134:
6133:
6128:
6110:
6108:
6107:
6102:
6100:
6093:
6089:
6088:
6083:
6063:
6021:
6020:
6004:
6000:
5999:
5994:
5974:
5933:
5932:
5899:
5897:
5896:
5891:
5889:
5884:
5864:
5848:
5821:
5820:
5798:
5796:
5795:
5790:
5769:
5767:
5766:
5761:
5749:
5747:
5746:
5741:
5721:
5719:
5718:
5713:
5701:
5699:
5698:
5693:
5668:
5666:
5665:
5660:
5658:
5653:
5639:
5627:
5625:
5624:
5619:
5614:
5613:
5606:
5601:
5581:
5566:
5561:
5543:
5542:
5535:
5530:
5516:
5495:
5490:
5466:
5465:
5443:
5441:
5440:
5435:
5423:
5421:
5420:
5415:
5390:
5388:
5387:
5382:
5371:
5370:
5351:
5349:
5348:
5343:
5295:
5293:
5292:
5287:
5285:
5284:
5283:
5273:
5256:
5239:
5238:
5237:
5232:
5216:
5215:
5214:
5201:
5184:
5170:
5153:
5133:
5132:
5131:
5126:
5109:
5107:
5106:
5101:
5099:
5098:
5097:
5087:
5070:
5053:
5052:
5051:
5046:
5030:
5029:
5028:
5015:
4998:
4984:
4967:
4947:
4946:
4945:
4940:
4913:
4911:
4910:
4905:
4903:
4902:
4897:
4888:
4883:
4880:
4871:
4863:
4862:
4861:
4856:
4846:
4845:
4844:
4838:
4825:
4823:
4822:
4817:
4815:
4814:
4809:
4800:
4795:
4792:
4783:
4775:
4774:
4773:
4768:
4758:
4757:
4756:
4750:
4729:symmetric matrix
4725:Hermitian matrix
4713:
4711:
4710:
4705:
4700:
4699:
4690:
4689:
4664:
4662:
4661:
4656:
4632:
4630:
4629:
4624:
4606:
4604:
4603:
4598:
4596:
4595:
4594:
4589:
4572:
4570:
4569:
4564:
4562:
4561:
4560:
4554:
4550:
4549:
4548:
4536:
4535:
4523:
4522:
4504:
4493:For example, if
4485:
4483:
4482:
4477:
4475:
4474:
4473:
4467:
4455:
4453:
4452:
4447:
4439:
4438:
4437:
4431:
4425:
4409:
4405:
4404:
4403:
4398:
4375:
4373:
4372:
4367:
4365:
4351:
4349:
4348:
4343:
4341:
4340:
4334:
4327:
4326:
4317:
4316:
4288:
4287:
4278:
4277:
4254:
4253:
4244:
4243:
4222:
4197:
4190:
4189:
4180:
4179:
4151:
4150:
4141:
4140:
4117:
4116:
4107:
4106:
4085:
4078:
4077:
4068:
4067:
4039:
4038:
4029:
4028:
4005:
4004:
3995:
3994:
3965:
3964:
3963:
3958:
3936:
3934:
3933:
3928:
3906:
3904:
3903:
3898:
3896:
3895:
3894:
3888:
3875:
3873:
3872:
3867:
3865:
3861:
3860:
3859:
3858:
3852:
3846:
3828:
3824:
3823:
3822:
3817:
3781:
3779:
3778:
3773:
3771:
3770:
3769:
3759:
3758:
3740:
3739:
3724:
3702:
3700:
3699:
3694:
3692:
3680:
3678:
3677:
3672:
3654:
3652:
3651:
3646:
3644:
3643:
3642:
3632:
3631:
3613:
3612:
3597:
3571:
3569:
3568:
3563:
3555:
3554:
3511:
3510:
3497:
3492:
3468:
3467:
3447:
3445:
3444:
3439:
3434:
3433:
3393:
3392:
3379:
3374:
3347:
3346:
3319:
3317:
3316:
3311:
3303:
3302:
3295:
3294:
3258:
3257:
3244:
3239:
3215:
3214:
3194:
3192:
3191:
3186:
3181:
3180:
3173:
3172:
3142:
3141:
3128:
3123:
3096:
3095:
3070:
3068:
3067:
3062:
3060:
3059:
3037:
3035:
3034:
3029:
3027:
3026:
2995:
2993:
2992:
2987:
2975:
2973:
2972:
2967:
2955:
2953:
2952:
2947:
2914:
2912:
2911:
2906:
2904:
2900:
2899:
2898:
2893:
2887:
2886:
2885:
2884:
2870:
2854:
2850:
2849:
2848:
2843:
2837:
2836:
2835:
2834:
2820:
2801:
2800:
2795:
2791:
2787:
2786:
2774:
2773:
2758:
2757:
2721:is always real.
2720:
2718:
2717:
2712:
2698:
2697:
2678:
2676:
2675:
2670:
2656:
2655:
2640:
2636:
2623:
2622:
2591:
2589:
2588:
2583:
2578:
2573:
2557:
2556:
2543:
2526:
2525:
2506:
2504:
2503:
2498:
2496:
2491:
2487:
2486:
2474:
2473:
2458:
2457:
2444:
2436:
2435:
2423:
2422:
2407:
2406:
2383:
2381:
2380:
2375:
2373:
2372:
2333:
2331:
2330:
2325:
2323:
2321:
2320:
2311:
2310:
2306:
2305:
2300:
2290:
2289:
2276:
2265:
2264:
2234:
2229:
2227:
2226:
2217:
2204:
2203:
2190:
2176:
2175:
2146:anti-correlation
2143:
2141:
2140:
2137:{\displaystyle }
2135:
2108:
2106:
2105:
2100:
2098:
2097:
2079:If the function
2076:
2074:
2073:
2068:
2063:
2061:
2060:
2059:
2058:
2057:
2043:
2042:
2041:
2040:
2025:
2024:
2020:
2019:
2014:
2010:
2009:
2008:
2007:
1990:
1989:
1988:
1987:
1969:
1964:
1963:
1962:
1961:
1944:
1943:
1942:
1941:
1912:
1907:
1905:
1904:
1903:
1902:
1901:
1887:
1886:
1885:
1884:
1869:
1865:
1864:
1852:
1851:
1836:
1835:
1822:
1814:
1813:
1801:
1800:
1788:
1787:
1748:
1746:
1745:
1740:
1735:
1734:
1710:
1709:
1685:
1683:
1682:
1677:
1675:
1667:
1659:
1655:
1654:
1653:
1648:
1640:
1637:
1636:
1607:
1603:
1602:
1597:
1587:
1586:
1573:
1562:
1561:
1517:
1516:
1487:
1485:
1484:
1479:
1477:
1473:
1472:
1471:
1466:
1458:
1455:
1454:
1413:
1412:
1387:
1385:
1384:
1379:
1377:
1376:
1364:
1363:
1337:
1335:
1334:
1329:
1327:
1326:
1310:
1308:
1307:
1302:
1300:
1299:
1283:
1281:
1280:
1275:
1273:
1272:
1256:
1254:
1253:
1248:
1232:
1230:
1229:
1224:
1222:
1218:
1217:
1181:
1179:
1178:
1173:
1171:
1170:
1169:
1168:
1158:
1150:
1147:
1146:
1145:
1144:
1127:
1123:
1122:
1121:
1120:
1119:
1109:
1101:
1098:
1097:
1096:
1095:
1067:
1063:
1062:
1057:
1053:
1052:
1051:
1050:
1033:
1032:
1031:
1030:
1012:
1007:
1006:
1005:
1004:
987:
986:
985:
984:
950:
949:
937:
936:
921:
920:
898:
896:
895:
890:
888:
887:
871:
869:
868:
863:
861:
860:
825:
823:
822:
817:
802:
800:
799:
794:
792:
788:
787:
786:
785:
784:
774:
766:
763:
762:
761:
760:
729:
728:
716:
715:
700:
699:
677:
675:
674:
669:
667:
666:
650:
648:
647:
642:
640:
639:
619:
617:
616:
611:
599:
597:
596:
591:
579:
577:
576:
571:
568:
563:
544:
542:
541:
536:
534:
533:
514:
512:
511:
506:
486:
484:
483:
478:
476:
475:
443:
441:
440:
435:
423:
421:
420:
415:
403:
401:
400:
395:
393:
389:
388:
272:
270:
269:
264:
246:
244:
243:
238:
220:
216:
212:
171:
164:
157:
41:
19:
18:
13523:
13522:
13518:
13517:
13516:
13514:
13513:
13512:
13498:Autocorrelation
13488:
13487:
13486:
13481:
13444:
13415:
13377:
13314:
13300:quality control
13267:
13249:Clinical trials
13226:
13201:
13185:
13173:Hazard function
13167:
13121:
13083:
13067:
13030:
13026:BreuschâGodfrey
13014:
12991:
12931:
12906:Factor analysis
12852:
12833:Graphical model
12805:
12772:
12739:
12725:
12705:
12659:
12626:
12588:
12551:
12550:
12519:
12463:
12450:
12442:
12434:
12418:
12403:
12382:Rank statistics
12376:
12355:Model selection
12343:
12301:Goodness of fit
12295:
12272:
12246:
12218:
12171:
12116:
12105:Median unbiased
12033:
11944:
11877:Order statistic
11839:
11818:
11785:
11759:
11711:
11666:
11609:
11607:Data collection
11588:
11500:
11455:
11429:
11407:
11367:
11319:
11236:Continuous data
11226:
11213:
11195:
11190:
11075:
11051:
11024:
11022:Further reading
11019:
11018:
11008:
11006:
11002:
10995:
10989:
10985:
10964:
10960:
10928:
10924:
10917:
10903:
10899:
10846:
10842:
10789:
10785:
10778:
10770:. Stata Press.
10764:
10760:
10747:
10746:
10742:
10719:
10715:
10708:
10686:
10682:
10675:
10661:
10657:
10607:
10603:
10596:
10582:
10578:
10571:
10557:
10553:
10546:
10532:
10528:
10521:
10507:
10500:
10491:
10482:
10470:
10455:
10448:
10434:
10417:
10412:
10407:
10311:
10278:
10275:
10274:
10254:
10250:
10241:
10237:
10232:
10229:
10228:
10203:
10199:
10195:
10193:
10190:
10189:
10170:
10167:
10166:
10146:
10143:
10142:
10139:random variable
10121:
10074:In analysis of
9965:surface science
9930:speckle pattern
9896:optical spectra
9877:
9850:
9847:
9846:
9815:
9812:
9811:
9771:
9768:
9767:
9736:
9733:
9732:
9688:
9684:
9682:
9679:
9678:
9677:distributed as
9630:standard errors
9575:
9554:
9551:
9550:
9534:
9531:
9530:
9506:
9502:
9479:
9475:
9459:
9455:
9450:
9447:
9446:
9420:
9416:
9399:
9395:
9385:
9381:
9376:
9373:
9372:
9349:
9346:
9345:
9323:
9320:
9319:
9308:biased estimate
9289:
9285:
9283:
9280:
9279:
9263:
9260:
9259:
9228:
9224:
9222:
9219:
9218:
9202:
9199:
9198:
9176:
9173:
9172:
9138:
9134:
9116:
9112:
9097:
9086:
9073:
9069:
9053:
9048:
9025:
9024:
9022:
9019:
9018:
8996:
8992:
8975:
8971:
8961:
8957:
8952:
8949:
8948:
8932:
8929:
8928:
8921:
8905:
8890:
8886:
8882:
8855:
8854:
8823:
8808:
8807:
8792:
8787:
8768:
8764:
8757:
8742:
8741:
8710:
8695:
8691:
8687:
8685:
8682:
8681:
8664:
8649:
8643:
8614:
8611:
8610:
8536:
8532:
8530:
8527:
8526:
8443:
8440:
8439:
8397:
8393:
8369:
8365:
8363:
8360:
8359:
8321:
8317:
8293:
8289:
8287:
8284:
8283:
8246:
8242:
8240:
8237:
8236:
8174:
8170:
8168:
8165:
8164:
8148:
8147:
8139:
8134:
8129:
8124:
8114:
8113:
8105:
8100:
8093:
8087:
8086:
8078:
8073:
8065:
8064:
8059:
8051:
8041:
8040:
8032:
8027:
8022:
8016:
8015:
8007:
8002:
7994:
7992:
7989:
7988:
7984:
7961:
7957:
7955:
7952:
7951:
7925:
7921:
7906:
7902:
7887:
7883:
7881:
7878:
7877:
7834:
7831:
7830:
7807:
7797:
7796:
7789:
7785:
7779:
7754:
7750:
7748:
7745:
7744:
7729:
7672:
7662:
7661:
7642:
7638:
7620:
7587:
7584:
7583:
7578:discrete signal
7566:
7525:
7513:
7509:
7479:
7475:
7473:
7470:
7469:
7440:
7436:
7434:
7431:
7430:
7374:
7370:
7368:
7365:
7364:
7348:
7345:
7344:
7324:
7320:
7318:
7315:
7314:
7294:
7291:
7290:
7264:
7261:
7260:
7217:
7213:
7205:
7187:
7183:
7178:
7176:
7173:
7172:
7156:
7153:
7152:
7127:
7124:
7123:
7097:
7089:
7061:
7057:
7055:
7052:
7051:
7029:
7026:
7025:
6996:
6992:
6968:
6964:
6962:
6959:
6958:
6920:
6916:
6895:
6891:
6889:
6886:
6885:
6873:
6826:
6824:
6798:
6794:
6793:
6786:
6782:
6781:
6756:
6752:
6750:
6747:
6746:
6705:
6703:
6671:
6667:
6666:
6659:
6655:
6654:
6629:
6625:
6623:
6620:
6619:
6601:
6598:
6597:
6571:
6567:
6558:
6554:
6549:
6546:
6545:
6529:
6526:
6525:
6506:
6503:
6502:
6486:
6483:
6482:
6466:
6463:
6462:
6459:
6427:
6426:
6398:
6396:
6371:
6360:
6346:
6334:
6323:
6305:
6301:
6298:
6297:
6288:
6287:
6267:
6265:
6241:
6236:
6222:
6210:
6199:
6181:
6177:
6173:
6171:
6168:
6167:
6142:
6139:
6138:
6122:
6119:
6118:
6098:
6097:
6064:
6062:
6048:
6044:
6031:
6013:
6009:
6006:
6005:
5975:
5973:
5960:
5956:
5943:
5925:
5921:
5917:
5915:
5912:
5911:
5901:
5865:
5863:
5838:
5813:
5809:
5807:
5804:
5803:
5775:
5772:
5771:
5755:
5752:
5751:
5735:
5732:
5731:
5728:
5707:
5704:
5703:
5678:
5675:
5674:
5669:represents the
5640:
5638:
5636:
5633:
5632:
5629:
5609:
5608:
5582:
5580:
5562:
5554:
5538:
5537:
5517:
5515:
5491:
5483:
5458:
5454:
5452:
5449:
5448:
5429:
5426:
5425:
5400:
5397:
5396:
5363:
5359:
5357:
5354:
5353:
5328:
5325:
5324:
5318:
5302:
5279:
5278:
5274:
5269:
5252:
5233:
5228:
5227:
5223:
5210:
5209:
5205:
5197:
5180:
5166:
5149:
5127:
5122:
5121:
5117:
5115:
5112:
5111:
5093:
5092:
5088:
5083:
5066:
5047:
5042:
5041:
5037:
5024:
5023:
5019:
5011:
4994:
4980:
4963:
4941:
4936:
4935:
4931:
4929:
4926:
4925:
4898:
4893:
4892:
4884:
4879:
4867:
4857:
4852:
4851:
4847:
4840:
4839:
4834:
4833:
4831:
4828:
4827:
4810:
4805:
4804:
4796:
4791:
4779:
4769:
4764:
4763:
4759:
4752:
4751:
4746:
4745:
4743:
4740:
4739:
4720:
4695:
4691:
4685:
4681:
4670:
4667:
4666:
4638:
4635:
4634:
4612:
4609:
4608:
4590:
4585:
4584:
4580:
4578:
4575:
4574:
4556:
4555:
4544:
4540:
4531:
4527:
4518:
4514:
4513:
4509:
4508:
4500:
4498:
4495:
4494:
4469:
4468:
4466:
4465:
4463:
4460:
4459:
4433:
4432:
4427:
4426:
4421:
4399:
4394:
4393:
4389:
4387:
4384:
4383:
4361:
4359:
4356:
4355:
4335:
4332:
4331:
4322:
4318:
4312:
4308:
4297:
4292:
4283:
4279:
4273:
4269:
4258:
4249:
4245:
4239:
4235:
4223:
4220:
4219:
4214:
4209:
4204:
4198:
4195:
4194:
4185:
4181:
4175:
4171:
4160:
4155:
4146:
4142:
4136:
4132:
4121:
4112:
4108:
4102:
4098:
4086:
4083:
4082:
4073:
4069:
4063:
4059:
4048:
4043:
4034:
4030:
4024:
4020:
4009:
4000:
3996:
3990:
3986:
3970:
3969:
3959:
3954:
3953:
3949:
3947:
3944:
3943:
3916:
3913:
3912:
3890:
3889:
3887:
3886:
3884:
3881:
3880:
3877:
3854:
3853:
3848:
3847:
3842:
3841:
3837:
3818:
3813:
3812:
3808:
3806:
3803:
3802:
3784:random elements
3765:
3764:
3760:
3754:
3750:
3735:
3731:
3720:
3718:
3715:
3714:
3688:
3686:
3683:
3682:
3660:
3657:
3656:
3638:
3637:
3633:
3627:
3623:
3608:
3604:
3593:
3591:
3588:
3587:
3577:
3550:
3549:
3503:
3499:
3493:
3485:
3460:
3456:
3454:
3451:
3450:
3429:
3428:
3385:
3381:
3375:
3367:
3339:
3335:
3333:
3330:
3329:
3298:
3297:
3275:
3271:
3250:
3246:
3240:
3232:
3207:
3203:
3201:
3198:
3197:
3176:
3175:
3156:
3152:
3134:
3130:
3124:
3116:
3088:
3084:
3082:
3079:
3078:
3052:
3048:
3046:
3043:
3042:
3019:
3015:
3013:
3010:
3009:
3002:
2981:
2978:
2977:
2961:
2958:
2957:
2935:
2932:
2931:
2920:
2894:
2889:
2888:
2880:
2876:
2875:
2871:
2866:
2865:
2861:
2844:
2839:
2838:
2830:
2826:
2825:
2821:
2816:
2815:
2811:
2796:
2782:
2778:
2769:
2765:
2750:
2746:
2745:
2741:
2740:
2738:
2735:
2734:
2727:
2690:
2686:
2684:
2681:
2680:
2648:
2644:
2615:
2611:
2610:
2606:
2604:
2601:
2600:
2597:
2595:Maximum at zero
2549:
2545:
2544:
2542:
2518:
2514:
2512:
2509:
2508:
2482:
2478:
2469:
2465:
2450:
2446:
2445:
2443:
2431:
2427:
2418:
2414:
2399:
2395:
2393:
2390:
2389:
2365:
2361:
2359:
2356:
2355:
2352:
2347:
2316:
2312:
2285:
2281:
2277:
2275:
2254:
2250:
2246:
2242:
2235:
2233:
2222:
2218:
2196:
2192:
2191:
2189:
2168:
2164:
2162:
2159:
2158:
2114:
2111:
2110:
2090:
2086:
2084:
2081:
2080:
2053:
2049:
2048:
2044:
2036:
2032:
2031:
2027:
2026:
2003:
1999:
1998:
1994:
1983:
1979:
1978:
1974:
1970:
1968:
1957:
1953:
1952:
1948:
1937:
1933:
1932:
1928:
1924:
1920:
1913:
1911:
1897:
1893:
1892:
1888:
1880:
1876:
1875:
1871:
1870:
1860:
1856:
1847:
1843:
1828:
1824:
1823:
1821:
1809:
1805:
1796:
1792:
1780:
1776:
1774:
1771:
1770:
1754:
1730:
1726:
1702:
1698:
1696:
1693:
1692:
1687:
1666:
1649:
1639:
1638:
1626:
1622:
1621:
1617:
1582:
1578:
1574:
1572:
1551:
1547:
1543:
1539:
1509:
1505:
1503:
1500:
1499:
1489:
1467:
1457:
1456:
1444:
1440:
1439:
1435:
1405:
1401:
1399:
1396:
1395:
1372:
1368:
1359:
1355:
1347:
1344:
1343:
1322:
1318:
1316:
1313:
1312:
1295:
1291:
1289:
1286:
1285:
1268:
1264:
1262:
1259:
1258:
1242:
1239:
1238:
1213:
1209:
1205:
1203:
1200:
1199:
1196:
1183:
1164:
1160:
1159:
1149:
1148:
1140:
1136:
1135:
1131:
1115:
1111:
1110:
1100:
1099:
1091:
1087:
1086:
1082:
1081:
1077:
1046:
1042:
1041:
1037:
1026:
1022:
1021:
1017:
1013:
1011:
1000:
996:
995:
991:
980:
976:
975:
971:
967:
963:
945:
941:
932:
928:
913:
909:
907:
904:
903:
883:
879:
877:
874:
873:
856:
852:
850:
847:
846:
811:
808:
807:
804:
780:
776:
775:
765:
764:
756:
752:
751:
747:
746:
742:
724:
720:
711:
707:
692:
688:
686:
683:
682:
662:
658:
656:
653:
652:
635:
631:
629:
626:
625:
605:
602:
601:
585:
582:
581:
564:
559:
553:
550:
549:
529:
525:
523:
520:
519:
500:
497:
496:
471:
467:
465:
462:
461:
460:process). Then
458:continuous-time
429:
426:
425:
409:
406:
405:
384:
380:
376:
374:
371:
370:
355:
302:periodic signal
298:random variable
278:Autocorrelation
252:
249:
248:
226:
223:
222:
218:
214:
210:
207:autocorrelation
175:
146:
145:
121:
111:
110:
86:
76:
75:
51:
17:
12:
11:
5:
13521:
13511:
13510:
13505:
13500:
13483:
13482:
13480:
13479:
13467:
13455:
13441:
13428:
13425:
13424:
13421:
13420:
13417:
13416:
13414:
13413:
13408:
13403:
13398:
13393:
13387:
13385:
13379:
13378:
13376:
13375:
13370:
13365:
13360:
13355:
13350:
13345:
13340:
13335:
13330:
13324:
13322:
13316:
13315:
13313:
13312:
13307:
13302:
13293:
13288:
13283:
13277:
13275:
13269:
13268:
13266:
13265:
13260:
13255:
13246:
13244:Bioinformatics
13240:
13238:
13228:
13227:
13215:
13214:
13211:
13210:
13207:
13206:
13203:
13202:
13200:
13199:
13193:
13191:
13187:
13186:
13184:
13183:
13177:
13175:
13169:
13168:
13166:
13165:
13160:
13155:
13150:
13144:
13142:
13133:
13127:
13126:
13123:
13122:
13120:
13119:
13114:
13109:
13104:
13099:
13093:
13091:
13085:
13084:
13082:
13081:
13076:
13071:
13063:
13058:
13053:
13052:
13051:
13049:partial (PACF)
13040:
13038:
13032:
13031:
13029:
13028:
13023:
13018:
13010:
13005:
12999:
12997:
12996:Specific tests
12993:
12992:
12990:
12989:
12984:
12979:
12974:
12969:
12964:
12959:
12954:
12948:
12946:
12939:
12933:
12932:
12930:
12929:
12928:
12927:
12926:
12925:
12910:
12909:
12908:
12898:
12896:Classification
12893:
12888:
12883:
12878:
12873:
12868:
12862:
12860:
12854:
12853:
12851:
12850:
12845:
12843:McNemar's test
12840:
12835:
12830:
12825:
12819:
12817:
12807:
12806:
12782:
12781:
12778:
12777:
12774:
12773:
12771:
12770:
12765:
12760:
12755:
12749:
12747:
12741:
12740:
12738:
12737:
12721:
12715:
12713:
12707:
12706:
12704:
12703:
12698:
12693:
12688:
12683:
12681:Semiparametric
12678:
12673:
12667:
12665:
12661:
12660:
12658:
12657:
12652:
12647:
12642:
12636:
12634:
12628:
12627:
12625:
12624:
12619:
12614:
12609:
12604:
12598:
12596:
12590:
12589:
12587:
12586:
12581:
12576:
12571:
12565:
12563:
12553:
12552:
12549:
12548:
12543:
12537:
12529:
12528:
12525:
12524:
12521:
12520:
12518:
12517:
12516:
12515:
12505:
12500:
12495:
12494:
12493:
12488:
12477:
12475:
12469:
12468:
12465:
12464:
12462:
12461:
12456:
12455:
12454:
12446:
12438:
12422:
12419:(MannâWhitney)
12414:
12413:
12412:
12399:
12398:
12397:
12386:
12384:
12378:
12377:
12375:
12374:
12373:
12372:
12367:
12362:
12352:
12347:
12344:(ShapiroâWilk)
12339:
12334:
12329:
12324:
12319:
12311:
12305:
12303:
12297:
12296:
12294:
12293:
12285:
12276:
12264:
12258:
12256:Specific tests
12252:
12251:
12248:
12247:
12245:
12244:
12239:
12234:
12228:
12226:
12220:
12219:
12217:
12216:
12211:
12210:
12209:
12199:
12198:
12197:
12187:
12181:
12179:
12173:
12172:
12170:
12169:
12168:
12167:
12162:
12152:
12147:
12142:
12137:
12132:
12126:
12124:
12118:
12117:
12115:
12114:
12109:
12108:
12107:
12102:
12101:
12100:
12095:
12080:
12079:
12078:
12073:
12068:
12063:
12052:
12050:
12041:
12035:
12034:
12032:
12031:
12026:
12021:
12020:
12019:
12009:
12004:
12003:
12002:
11992:
11991:
11990:
11985:
11980:
11970:
11965:
11960:
11959:
11958:
11953:
11948:
11932:
11931:
11930:
11925:
11920:
11910:
11909:
11908:
11903:
11893:
11892:
11891:
11881:
11880:
11879:
11869:
11864:
11859:
11853:
11851:
11841:
11840:
11828:
11827:
11824:
11823:
11820:
11819:
11817:
11816:
11811:
11806:
11801:
11795:
11793:
11787:
11786:
11784:
11783:
11778:
11773:
11767:
11765:
11761:
11760:
11758:
11757:
11752:
11747:
11742:
11737:
11732:
11727:
11721:
11719:
11713:
11712:
11710:
11709:
11707:Standard error
11704:
11699:
11694:
11693:
11692:
11687:
11676:
11674:
11668:
11667:
11665:
11664:
11659:
11654:
11649:
11644:
11639:
11637:Optimal design
11634:
11629:
11623:
11621:
11611:
11610:
11598:
11597:
11594:
11593:
11590:
11589:
11587:
11586:
11581:
11576:
11571:
11566:
11561:
11556:
11551:
11546:
11541:
11536:
11531:
11526:
11521:
11516:
11510:
11508:
11502:
11501:
11499:
11498:
11493:
11492:
11491:
11486:
11476:
11471:
11465:
11463:
11457:
11456:
11454:
11453:
11448:
11443:
11437:
11435:
11434:Summary tables
11431:
11430:
11428:
11427:
11421:
11419:
11413:
11412:
11409:
11408:
11406:
11405:
11404:
11403:
11398:
11393:
11383:
11377:
11375:
11369:
11368:
11366:
11365:
11360:
11355:
11350:
11345:
11340:
11335:
11329:
11327:
11321:
11320:
11318:
11317:
11312:
11307:
11306:
11305:
11300:
11295:
11290:
11285:
11280:
11275:
11270:
11268:Contraharmonic
11265:
11260:
11249:
11247:
11238:
11228:
11227:
11215:
11214:
11212:
11211:
11206:
11200:
11197:
11196:
11189:
11188:
11181:
11174:
11166:
11160:
11159:
11140:
11123:
11112:
11079:
11073:
11055:
11049:
11023:
11020:
11017:
11016:
10983:
10958:
10922:
10915:
10897:
10840:
10783:
10776:
10758:
10755:. 26 May 2014.
10740:
10729:(4): 274â276.
10713:
10706:
10680:
10674:978-0125649018
10673:
10655:
10601:
10595:978-0122673511
10594:
10576:
10570:978-0130607744
10569:
10551:
10545:978-0130617934
10544:
10526:
10519:
10498:
10480:
10453:
10446:
10414:
10413:
10411:
10408:
10406:
10405:
10400:
10395:
10390:
10385:
10380:
10374:
10369:
10364:
10359:
10354:
10349:
10344:
10339:
10333:
10331:Autocorrelator
10328:
10323:
10318:
10312:
10310:
10307:
10294:
10291:
10288:
10285:
10282:
10262:
10257:
10253:
10249:
10244:
10240:
10236:
10211:
10206:
10202:
10198:
10174:
10150:
10120:
10117:
10116:
10115:
10108:
10105:rate of return
10097:
10090:
10079:
10072:
10065:
10062:X-ray binaries
10050:
10031:
10024:
10017:
9994:
9979:
9972:
9961:
9954:
9946:carrier signal
9934:
9914:
9892:
9876:
9873:
9860:
9857:
9854:
9834:
9831:
9828:
9825:
9822:
9819:
9799:
9796:
9793:
9790:
9787:
9784:
9781:
9778:
9775:
9755:
9752:
9749:
9746:
9743:
9740:
9691:
9687:
9657:test statistic
9574:
9571:
9558:
9538:
9527:
9526:
9514:
9509:
9505:
9500:
9497:
9493:
9488:
9485:
9482:
9478:
9473:
9468:
9465:
9462:
9458:
9454:
9434:
9429:
9426:
9423:
9419:
9414:
9411:
9407:
9402:
9398:
9393:
9388:
9384:
9380:
9369:
9353:
9333:
9330:
9327:
9312:
9292:
9288:
9267:
9231:
9227:
9206:
9186:
9183:
9180:
9158:
9155:
9152:
9147:
9144:
9141:
9137:
9133:
9130:
9127:
9124:
9119:
9115:
9111:
9106:
9103:
9100:
9095:
9092:
9089:
9085:
9076:
9072:
9068:
9065:
9062:
9059:
9056:
9052:
9047:
9044:
9041:
9038:
9032:
9029:
9004:
8999:
8995:
8990:
8987:
8983:
8978:
8974:
8969:
8964:
8960:
8956:
8936:
8920:
8917:
8853:
8850:
8847:
8844:
8841:
8838:
8835:
8832:
8829:
8826:
8824:
8822:
8819:
8816:
8813:
8810:
8809:
8806:
8803:
8800:
8795:
8790:
8786:
8782:
8779:
8776:
8771:
8767:
8763:
8760:
8758:
8756:
8753:
8750:
8747:
8744:
8743:
8740:
8737:
8734:
8731:
8728:
8725:
8722:
8719:
8716:
8713:
8711:
8709:
8706:
8703:
8698:
8694:
8690:
8689:
8621:
8618:
8598:
8595:
8592:
8589:
8586:
8583:
8580:
8577:
8574:
8571:
8568:
8565:
8562:
8559:
8556:
8553:
8550:
8547:
8542:
8539:
8535:
8510:
8507:
8504:
8501:
8498:
8495:
8492:
8489:
8486:
8483:
8480:
8477:
8474:
8471:
8468:
8465:
8462:
8459:
8456:
8453:
8450:
8447:
8426:
8423:
8420:
8417:
8414:
8411:
8408:
8403:
8400:
8396:
8392:
8389:
8386:
8383:
8380:
8375:
8372:
8368:
8347:
8344:
8341:
8338:
8335:
8332:
8327:
8324:
8320:
8316:
8313:
8310:
8307:
8304:
8299:
8296:
8292:
8272:
8269:
8266:
8263:
8260:
8257:
8252:
8249:
8245:
8224:
8221:
8218:
8215:
8212:
8209:
8206:
8203:
8200:
8197:
8194:
8191:
8188:
8185:
8180:
8177:
8173:
8146:
8143:
8140:
8138:
8135:
8133:
8130:
8128:
8125:
8123:
8120:
8117:
8115:
8112:
8109:
8106:
8104:
8101:
8099:
8096:
8092:
8089:
8088:
8085:
8082:
8079:
8077:
8074:
8072:
8069:
8066:
8063:
8060:
8058:
8055:
8052:
8050:
8047:
8044:
8042:
8039:
8036:
8033:
8031:
8028:
8026:
8023:
8021:
8018:
8017:
8014:
8011:
8008:
8006:
8003:
8001:
7998:
7996:
7972:
7969:
7964:
7960:
7939:
7936:
7933:
7928:
7924:
7920:
7917:
7914:
7909:
7905:
7901:
7898:
7895:
7890:
7886:
7865:
7862:
7859:
7856:
7853:
7850:
7847:
7844:
7841:
7838:
7816:
7813:
7810:
7804:
7801:
7792:
7788:
7782:
7778:
7774:
7771:
7768:
7765:
7760:
7757:
7753:
7728:
7725:
7710:
7705:
7702:
7699:
7696:
7693:
7690:
7687:
7684:
7681:
7678:
7675:
7669:
7666:
7657:
7654:
7651:
7648:
7645:
7641:
7635:
7632:
7629:
7626:
7623:
7619:
7615:
7612:
7609:
7606:
7603:
7600:
7597:
7594:
7591:
7565:
7562:
7561:
7560:
7549:
7546:
7543:
7540:
7537:
7532:
7529:
7524:
7519:
7516:
7512:
7508:
7505:
7502:
7499:
7496:
7493:
7490:
7485:
7482:
7478:
7457:
7454:
7451:
7446:
7443:
7439:
7418:
7415:
7412:
7409:
7406:
7403:
7400:
7397:
7394:
7391:
7388:
7385:
7380:
7377:
7373:
7352:
7330:
7327:
7323:
7298:
7287:
7280:
7268:
7257:
7250:
7234:
7231:
7228:
7223:
7220:
7216:
7212:
7208:
7204:
7201:
7198:
7193:
7190:
7186:
7181:
7160:
7149:
7148:
7147:
7131:
7111:
7108:
7105:
7100:
7095:
7092:
7088:
7084:
7081:
7078:
7075:
7072:
7067:
7064:
7060:
7045:
7033:
7013:
7010:
7007:
7002:
6999:
6995:
6991:
6988:
6985:
6982:
6979:
6974:
6971:
6967:
6940:
6937:
6934:
6931:
6926:
6923:
6919:
6915:
6912:
6909:
6906:
6901:
6898:
6894:
6872:
6869:
6857:
6854:
6848:
6844:
6841:
6838:
6835:
6832:
6829:
6823:
6820:
6817:
6814:
6809:
6806:
6801:
6797:
6789:
6785:
6780:
6776:
6773:
6770:
6767:
6762:
6759:
6755:
6730:
6727:
6721:
6717:
6714:
6711:
6708:
6702:
6699:
6696:
6693:
6690:
6687:
6682:
6679:
6674:
6670:
6662:
6658:
6653:
6649:
6646:
6643:
6640:
6635:
6632:
6628:
6605:
6585:
6582:
6579:
6574:
6570:
6566:
6561:
6557:
6553:
6533:
6513:
6510:
6490:
6470:
6458:
6455:
6425:
6420:
6416:
6413:
6410:
6407:
6404:
6401:
6394:
6391:
6388:
6385:
6380:
6377:
6374:
6369:
6366:
6363:
6359:
6353:
6350:
6343:
6340:
6337:
6333:
6329:
6326:
6324:
6322:
6319:
6316:
6311:
6308:
6304:
6300:
6299:
6296:
6291:
6283:
6279:
6276:
6273:
6270:
6264:
6261:
6258:
6255:
6252:
6249:
6244:
6239:
6235:
6229:
6226:
6219:
6216:
6213:
6209:
6205:
6202:
6200:
6198:
6195:
6192:
6187:
6184:
6180:
6176:
6175:
6146:
6126:
6096:
6092:
6086:
6082:
6079:
6076:
6073:
6070:
6067:
6060:
6057:
6054:
6051:
6047:
6043:
6040:
6037:
6034:
6032:
6030:
6027:
6024:
6019:
6016:
6012:
6008:
6007:
6003:
5997:
5993:
5990:
5987:
5984:
5981:
5978:
5972:
5969:
5966:
5963:
5959:
5955:
5952:
5949:
5946:
5944:
5942:
5939:
5936:
5931:
5928:
5924:
5920:
5919:
5887:
5883:
5880:
5877:
5874:
5871:
5868:
5861:
5858:
5855:
5852:
5847:
5844:
5841:
5837:
5833:
5830:
5827:
5824:
5819:
5816:
5812:
5801:
5788:
5785:
5782:
5779:
5759:
5739:
5727:
5724:
5711:
5691:
5688:
5685:
5682:
5656:
5652:
5649:
5646:
5643:
5617:
5612:
5604:
5600:
5597:
5594:
5591:
5588:
5585:
5579:
5576:
5573:
5570:
5565:
5560:
5557:
5553:
5549:
5546:
5541:
5533:
5529:
5526:
5523:
5520:
5514:
5511:
5508:
5505:
5502:
5499:
5494:
5489:
5486:
5482:
5478:
5475:
5472:
5469:
5464:
5461:
5457:
5446:
5433:
5413:
5410:
5407:
5404:
5380:
5377:
5374:
5369:
5366:
5362:
5341:
5338:
5335:
5332:
5317:
5314:
5301:
5298:
5297:
5296:
5282:
5277:
5272:
5268:
5265:
5262:
5259:
5255:
5251:
5248:
5245:
5242:
5236:
5231:
5226:
5222:
5219:
5213:
5208:
5204:
5200:
5196:
5193:
5190:
5187:
5183:
5179:
5176:
5173:
5169:
5165:
5162:
5159:
5156:
5152:
5148:
5145:
5142:
5139:
5136:
5130:
5125:
5120:
5096:
5091:
5086:
5082:
5079:
5076:
5073:
5069:
5065:
5062:
5059:
5056:
5050:
5045:
5040:
5036:
5033:
5027:
5022:
5018:
5014:
5010:
5007:
5004:
5001:
4997:
4993:
4990:
4987:
4983:
4979:
4976:
4973:
4970:
4966:
4962:
4959:
4956:
4953:
4950:
4944:
4939:
4934:
4918:
4915:
4901:
4896:
4891:
4887:
4877:
4874:
4870:
4866:
4860:
4855:
4850:
4843:
4837:
4813:
4808:
4803:
4799:
4789:
4786:
4782:
4778:
4772:
4767:
4762:
4755:
4749:
4732:
4719:
4716:
4703:
4698:
4694:
4688:
4684:
4680:
4677:
4674:
4654:
4651:
4648:
4645:
4642:
4622:
4619:
4616:
4593:
4588:
4583:
4559:
4553:
4547:
4543:
4539:
4534:
4530:
4526:
4521:
4517:
4512:
4507:
4503:
4472:
4445:
4442:
4436:
4430:
4424:
4420:
4417:
4414:
4408:
4402:
4397:
4392:
4364:
4339:
4333:
4330:
4325:
4321:
4315:
4311:
4307:
4304:
4301:
4298:
4296:
4293:
4291:
4286:
4282:
4276:
4272:
4268:
4265:
4262:
4259:
4257:
4252:
4248:
4242:
4238:
4234:
4231:
4228:
4225:
4224:
4221:
4218:
4215:
4213:
4210:
4208:
4205:
4203:
4200:
4199:
4196:
4193:
4188:
4184:
4178:
4174:
4170:
4167:
4164:
4161:
4159:
4156:
4154:
4149:
4145:
4139:
4135:
4131:
4128:
4125:
4122:
4120:
4115:
4111:
4105:
4101:
4097:
4094:
4091:
4088:
4087:
4084:
4081:
4076:
4072:
4066:
4062:
4058:
4055:
4052:
4049:
4047:
4044:
4042:
4037:
4033:
4027:
4023:
4019:
4016:
4013:
4010:
4008:
4003:
3999:
3993:
3989:
3985:
3982:
3979:
3976:
3975:
3973:
3968:
3962:
3957:
3952:
3926:
3923:
3920:
3893:
3864:
3857:
3851:
3845:
3840:
3836:
3833:
3827:
3821:
3816:
3811:
3800:
3798:is defined by
3788:expected value
3768:
3763:
3757:
3753:
3749:
3746:
3743:
3738:
3734:
3730:
3727:
3723:
3691:
3670:
3667:
3664:
3641:
3636:
3630:
3626:
3622:
3619:
3616:
3611:
3607:
3603:
3600:
3596:
3576:
3573:
3561:
3558:
3553:
3547:
3544:
3541:
3538:
3535:
3532:
3529:
3526:
3523:
3520:
3517:
3514:
3509:
3506:
3502:
3496:
3491:
3488:
3484:
3480:
3477:
3474:
3471:
3466:
3463:
3459:
3437:
3432:
3426:
3423:
3420:
3417:
3414:
3411:
3408:
3405:
3402:
3399:
3396:
3391:
3388:
3384:
3378:
3373:
3370:
3366:
3362:
3359:
3356:
3353:
3350:
3345:
3342:
3338:
3309:
3306:
3301:
3293:
3290:
3287:
3284:
3281:
3278:
3274:
3270:
3267:
3264:
3261:
3256:
3253:
3249:
3243:
3238:
3235:
3231:
3227:
3224:
3221:
3218:
3213:
3210:
3206:
3184:
3179:
3171:
3168:
3165:
3162:
3159:
3155:
3151:
3148:
3145:
3140:
3137:
3133:
3127:
3122:
3119:
3115:
3111:
3108:
3105:
3102:
3099:
3094:
3091:
3087:
3058:
3055:
3051:
3025:
3022:
3018:
3001:
2998:
2985:
2976:for all other
2965:
2945:
2942:
2939:
2919:
2916:
2903:
2897:
2892:
2883:
2879:
2874:
2869:
2864:
2860:
2857:
2853:
2847:
2842:
2833:
2829:
2824:
2819:
2814:
2810:
2807:
2804:
2799:
2794:
2790:
2785:
2781:
2777:
2772:
2768:
2764:
2761:
2756:
2753:
2749:
2744:
2726:
2723:
2710:
2707:
2704:
2701:
2696:
2693:
2689:
2668:
2665:
2662:
2659:
2654:
2651:
2647:
2643:
2639:
2635:
2632:
2629:
2626:
2621:
2618:
2614:
2609:
2596:
2593:
2581:
2576:
2572:
2569:
2566:
2563:
2560:
2555:
2552:
2548:
2541:
2538:
2535:
2532:
2529:
2524:
2521:
2517:
2494:
2490:
2485:
2481:
2477:
2472:
2468:
2464:
2461:
2456:
2453:
2449:
2442:
2439:
2434:
2430:
2426:
2421:
2417:
2413:
2410:
2405:
2402:
2398:
2371:
2368:
2364:
2351:
2348:
2346:
2343:
2319:
2315:
2309:
2303:
2299:
2296:
2293:
2288:
2284:
2280:
2274:
2271:
2268:
2263:
2260:
2257:
2253:
2249:
2245:
2241:
2238:
2232:
2225:
2221:
2216:
2213:
2210:
2207:
2202:
2199:
2195:
2188:
2185:
2182:
2179:
2174:
2171:
2167:
2133:
2130:
2127:
2124:
2121:
2118:
2096:
2093:
2089:
2066:
2056:
2052:
2047:
2039:
2035:
2030:
2023:
2017:
2013:
2006:
2002:
1997:
1993:
1986:
1982:
1977:
1973:
1967:
1960:
1956:
1951:
1947:
1940:
1936:
1931:
1927:
1923:
1919:
1916:
1910:
1900:
1896:
1891:
1883:
1879:
1874:
1868:
1863:
1859:
1855:
1850:
1846:
1842:
1839:
1834:
1831:
1827:
1820:
1817:
1812:
1808:
1804:
1799:
1795:
1791:
1786:
1783:
1779:
1753:
1750:
1738:
1733:
1729:
1725:
1722:
1719:
1716:
1713:
1708:
1705:
1701:
1673:
1670:
1665:
1662:
1658:
1652:
1646:
1643:
1635:
1632:
1629:
1625:
1620:
1616:
1613:
1610:
1606:
1600:
1596:
1593:
1590:
1585:
1581:
1577:
1571:
1568:
1565:
1560:
1557:
1554:
1550:
1546:
1542:
1538:
1535:
1532:
1529:
1526:
1523:
1520:
1515:
1512:
1508:
1497:
1476:
1470:
1464:
1461:
1453:
1450:
1447:
1443:
1438:
1434:
1431:
1428:
1425:
1422:
1419:
1416:
1411:
1408:
1404:
1393:
1375:
1371:
1367:
1362:
1358:
1354:
1351:
1325:
1321:
1298:
1294:
1271:
1267:
1246:
1237:then the mean
1221:
1216:
1212:
1208:
1195:
1192:
1167:
1163:
1156:
1153:
1143:
1139:
1134:
1130:
1126:
1118:
1114:
1107:
1104:
1094:
1090:
1085:
1080:
1076:
1073:
1070:
1066:
1060:
1056:
1049:
1045:
1040:
1036:
1029:
1025:
1020:
1016:
1010:
1003:
999:
994:
990:
983:
979:
974:
970:
966:
962:
959:
956:
953:
948:
944:
940:
935:
931:
927:
924:
919:
916:
912:
901:
886:
882:
859:
855:
845:between times
828:expected value
815:
791:
783:
779:
772:
769:
759:
755:
750:
745:
741:
738:
735:
732:
727:
723:
719:
714:
710:
706:
703:
698:
695:
691:
680:
665:
661:
638:
634:
624:between times
609:
589:
567:
562:
558:
532:
528:
504:
474:
470:
433:
413:
392:
387:
383:
379:
363:random process
354:
351:
329:autocovariance
262:
259:
256:
236:
233:
230:
221:is the reason
177:
176:
174:
173:
166:
159:
151:
148:
147:
144:
143:
138:
133:
128:
122:
117:
116:
113:
112:
109:
108:
103:
98:
93:
87:
82:
81:
78:
77:
74:
73:
68:
63:
58:
52:
47:
46:
43:
42:
34:
33:
27:
26:
15:
9:
6:
4:
3:
2:
13520:
13509:
13506:
13504:
13501:
13499:
13496:
13495:
13493:
13478:
13477:
13468:
13466:
13465:
13456:
13454:
13453:
13448:
13442:
13440:
13439:
13430:
13429:
13426:
13412:
13409:
13407:
13406:Geostatistics
13404:
13402:
13399:
13397:
13394:
13392:
13389:
13388:
13386:
13384:
13380:
13374:
13373:Psychometrics
13371:
13369:
13366:
13364:
13361:
13359:
13356:
13354:
13351:
13349:
13346:
13344:
13341:
13339:
13336:
13334:
13331:
13329:
13326:
13325:
13323:
13321:
13317:
13311:
13308:
13306:
13303:
13301:
13297:
13294:
13292:
13289:
13287:
13284:
13282:
13279:
13278:
13276:
13274:
13270:
13264:
13261:
13259:
13256:
13254:
13250:
13247:
13245:
13242:
13241:
13239:
13237:
13236:Biostatistics
13233:
13229:
13225:
13220:
13216:
13198:
13197:Log-rank test
13195:
13194:
13192:
13188:
13182:
13179:
13178:
13176:
13174:
13170:
13164:
13161:
13159:
13156:
13154:
13151:
13149:
13146:
13145:
13143:
13141:
13137:
13134:
13132:
13128:
13118:
13115:
13113:
13110:
13108:
13105:
13103:
13100:
13098:
13095:
13094:
13092:
13090:
13086:
13080:
13077:
13075:
13072:
13070:
13068:(BoxâJenkins)
13064:
13062:
13059:
13057:
13054:
13050:
13047:
13046:
13045:
13042:
13041:
13039:
13037:
13033:
13027:
13024:
13022:
13021:DurbinâWatson
13019:
13017:
13011:
13009:
13006:
13004:
13003:DickeyâFuller
13001:
13000:
12998:
12994:
12988:
12985:
12983:
12980:
12978:
12977:Cointegration
12975:
12973:
12970:
12968:
12965:
12963:
12960:
12958:
12955:
12953:
12952:Decomposition
12950:
12949:
12947:
12943:
12940:
12938:
12934:
12924:
12921:
12920:
12919:
12916:
12915:
12914:
12911:
12907:
12904:
12903:
12902:
12899:
12897:
12894:
12892:
12889:
12887:
12884:
12882:
12879:
12877:
12874:
12872:
12869:
12867:
12864:
12863:
12861:
12859:
12855:
12849:
12846:
12844:
12841:
12839:
12836:
12834:
12831:
12829:
12826:
12824:
12823:Cohen's kappa
12821:
12820:
12818:
12816:
12812:
12808:
12804:
12800:
12796:
12792:
12787:
12783:
12769:
12766:
12764:
12761:
12759:
12756:
12754:
12751:
12750:
12748:
12746:
12742:
12736:
12732:
12728:
12722:
12720:
12717:
12716:
12714:
12712:
12708:
12702:
12699:
12697:
12694:
12692:
12689:
12687:
12684:
12682:
12679:
12677:
12676:Nonparametric
12674:
12672:
12669:
12668:
12666:
12662:
12656:
12653:
12651:
12648:
12646:
12643:
12641:
12638:
12637:
12635:
12633:
12629:
12623:
12620:
12618:
12615:
12613:
12610:
12608:
12605:
12603:
12600:
12599:
12597:
12595:
12591:
12585:
12582:
12580:
12577:
12575:
12572:
12570:
12567:
12566:
12564:
12562:
12558:
12554:
12547:
12544:
12542:
12539:
12538:
12534:
12530:
12514:
12511:
12510:
12509:
12506:
12504:
12501:
12499:
12496:
12492:
12489:
12487:
12484:
12483:
12482:
12479:
12478:
12476:
12474:
12470:
12460:
12457:
12453:
12447:
12445:
12439:
12437:
12431:
12430:
12429:
12426:
12425:Nonparametric
12423:
12421:
12415:
12411:
12408:
12407:
12406:
12400:
12396:
12395:Sample median
12393:
12392:
12391:
12388:
12387:
12385:
12383:
12379:
12371:
12368:
12366:
12363:
12361:
12358:
12357:
12356:
12353:
12351:
12348:
12346:
12340:
12338:
12335:
12333:
12330:
12328:
12325:
12323:
12320:
12318:
12316:
12312:
12310:
12307:
12306:
12304:
12302:
12298:
12292:
12290:
12286:
12284:
12282:
12277:
12275:
12270:
12266:
12265:
12262:
12259:
12257:
12253:
12243:
12240:
12238:
12235:
12233:
12230:
12229:
12227:
12225:
12221:
12215:
12212:
12208:
12205:
12204:
12203:
12200:
12196:
12193:
12192:
12191:
12188:
12186:
12183:
12182:
12180:
12178:
12174:
12166:
12163:
12161:
12158:
12157:
12156:
12153:
12151:
12148:
12146:
12143:
12141:
12138:
12136:
12133:
12131:
12128:
12127:
12125:
12123:
12119:
12113:
12110:
12106:
12103:
12099:
12096:
12094:
12091:
12090:
12089:
12086:
12085:
12084:
12081:
12077:
12074:
12072:
12069:
12067:
12064:
12062:
12059:
12058:
12057:
12054:
12053:
12051:
12049:
12045:
12042:
12040:
12036:
12030:
12027:
12025:
12022:
12018:
12015:
12014:
12013:
12010:
12008:
12005:
12001:
12000:loss function
11998:
11997:
11996:
11993:
11989:
11986:
11984:
11981:
11979:
11976:
11975:
11974:
11971:
11969:
11966:
11964:
11961:
11957:
11954:
11952:
11949:
11947:
11941:
11938:
11937:
11936:
11933:
11929:
11926:
11924:
11921:
11919:
11916:
11915:
11914:
11911:
11907:
11904:
11902:
11899:
11898:
11897:
11894:
11890:
11887:
11886:
11885:
11882:
11878:
11875:
11874:
11873:
11870:
11868:
11865:
11863:
11860:
11858:
11855:
11854:
11852:
11850:
11846:
11842:
11838:
11833:
11829:
11815:
11812:
11810:
11807:
11805:
11802:
11800:
11797:
11796:
11794:
11792:
11788:
11782:
11779:
11777:
11774:
11772:
11769:
11768:
11766:
11762:
11756:
11753:
11751:
11748:
11746:
11743:
11741:
11738:
11736:
11733:
11731:
11728:
11726:
11723:
11722:
11720:
11718:
11714:
11708:
11705:
11703:
11702:Questionnaire
11700:
11698:
11695:
11691:
11688:
11686:
11683:
11682:
11681:
11678:
11677:
11675:
11673:
11669:
11663:
11660:
11658:
11655:
11653:
11650:
11648:
11645:
11643:
11640:
11638:
11635:
11633:
11630:
11628:
11625:
11624:
11622:
11620:
11616:
11612:
11608:
11603:
11599:
11585:
11582:
11580:
11577:
11575:
11572:
11570:
11567:
11565:
11562:
11560:
11557:
11555:
11552:
11550:
11547:
11545:
11542:
11540:
11537:
11535:
11532:
11530:
11529:Control chart
11527:
11525:
11522:
11520:
11517:
11515:
11512:
11511:
11509:
11507:
11503:
11497:
11494:
11490:
11487:
11485:
11482:
11481:
11480:
11477:
11475:
11472:
11470:
11467:
11466:
11464:
11462:
11458:
11452:
11449:
11447:
11444:
11442:
11439:
11438:
11436:
11432:
11426:
11423:
11422:
11420:
11418:
11414:
11402:
11399:
11397:
11394:
11392:
11389:
11388:
11387:
11384:
11382:
11379:
11378:
11376:
11374:
11370:
11364:
11361:
11359:
11356:
11354:
11351:
11349:
11346:
11344:
11341:
11339:
11336:
11334:
11331:
11330:
11328:
11326:
11322:
11316:
11313:
11311:
11308:
11304:
11301:
11299:
11296:
11294:
11291:
11289:
11286:
11284:
11281:
11279:
11276:
11274:
11271:
11269:
11266:
11264:
11261:
11259:
11256:
11255:
11254:
11251:
11250:
11248:
11246:
11242:
11239:
11237:
11233:
11229:
11225:
11220:
11216:
11210:
11207:
11205:
11202:
11201:
11198:
11194:
11187:
11182:
11180:
11175:
11173:
11168:
11167:
11164:
11155:
11154:
11149:
11146:
11141:
11138:
11137:9780128133477
11134:
11130:
11129:
11124:
11121:
11117:
11113:
11109:
11105:
11101:
11097:
11093:
11089:
11085:
11080:
11076:
11070:
11066:
11065:
11060:
11059:Marno Verbeek
11056:
11052:
11046:
11042:
11037:
11036:
11030:
11026:
11025:
11001:
10994:
10987:
10979:
10975:
10974:
10969:
10962:
10954:
10950:
10946:
10942:
10938:
10934:
10926:
10918:
10912:
10908:
10901:
10893:
10889:
10885:
10881:
10876:
10871:
10867:
10863:
10859:
10855:
10851:
10844:
10836:
10832:
10827:
10822:
10818:
10814:
10810:
10806:
10802:
10798:
10794:
10787:
10779:
10773:
10769:
10762:
10754:
10750:
10744:
10736:
10732:
10728:
10724:
10717:
10709:
10703:
10699:
10694:
10693:
10684:
10676:
10670:
10666:
10659:
10651:
10647:
10643:
10639:
10635:
10631:
10626:
10621:
10617:
10614:
10613:
10605:
10597:
10591:
10587:
10580:
10572:
10566:
10562:
10555:
10547:
10541:
10537:
10530:
10522:
10516:
10512:
10505:
10503:
10495:
10489:
10487:
10485:
10478:
10474:
10468:
10466:
10464:
10462:
10460:
10458:
10449:
10443:
10439:
10432:
10430:
10428:
10426:
10424:
10422:
10420:
10415:
10404:
10401:
10399:
10396:
10394:
10391:
10389:
10386:
10384:
10381:
10378:
10375:
10373:
10370:
10368:
10365:
10363:
10360:
10358:
10355:
10353:
10350:
10348:
10345:
10343:
10340:
10337:
10334:
10332:
10329:
10327:
10324:
10322:
10319:
10317:
10314:
10313:
10306:
10292:
10289:
10286:
10283:
10280:
10255:
10251:
10247:
10242:
10238:
10226:
10209:
10204:
10200:
10196:
10186:
10172:
10164:
10148:
10140:
10136:
10131:
10129:
10125:
10113:
10109:
10106:
10102:
10098:
10095:
10091:
10088:
10084:
10080:
10077:
10073:
10070:
10066:
10063:
10059:
10055:
10051:
10048:
10044:
10040:
10036:
10032:
10029:
10025:
10022:
10018:
10015:
10011:
10007:
10003:
9999:
9995:
9992:
9988:
9984:
9980:
9977:
9973:
9970:
9966:
9962:
9959:
9955:
9952:
9951:doppler shift
9947:
9943:
9939:
9935:
9931:
9927:
9923:
9919:
9915:
9912:
9909:, both using
9908:
9904:
9901:
9897:
9893:
9890:
9886:
9885:
9884:
9882:
9872:
9858:
9855:
9852:
9832:
9829:
9823:
9817:
9797:
9794:
9791:
9788:
9785:
9782:
9779:
9776:
9773:
9753:
9750:
9744:
9738:
9730:
9726:
9721:
9719:
9715:
9710:
9708:
9704:
9689:
9685:
9674:
9670:
9666:
9662:
9658:
9654:
9650:
9646:
9642:
9637:
9635:
9631:
9627:
9623:
9619:
9615:
9611:
9606:
9604:
9600:
9596:
9592:
9588:
9584:
9580:
9570:
9556:
9536:
9507:
9503:
9498:
9495:
9491:
9486:
9483:
9480:
9476:
9471:
9466:
9463:
9460:
9456:
9427:
9424:
9421:
9417:
9412:
9409:
9405:
9400:
9396:
9391:
9386:
9382:
9370:
9367:
9351:
9331:
9328:
9325:
9317:
9313:
9310:
9309:
9290:
9286:
9265:
9257:
9256:
9255:
9253:
9249:
9248:
9229:
9225:
9217:and variance
9204:
9184:
9181:
9178:
9169:
9153:
9150:
9145:
9142:
9139:
9135:
9125:
9122:
9117:
9113:
9104:
9101:
9098:
9093:
9090:
9087:
9083:
9074:
9070:
9063:
9060:
9057:
9050:
9045:
9039:
9027:
9016:
8997:
8993:
8988:
8985:
8981:
8976:
8972:
8967:
8962:
8958:
8947:observations
8934:
8926:
8916:
8912:
8908:
8903:
8897:
8893:
8879:
8877:
8873:
8868:
8845:
8839:
8833:
8830:
8827:
8825:
8817:
8811:
8801:
8793:
8788:
8784:
8777:
8769:
8765:
8761:
8759:
8751:
8745:
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8308:
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8198:
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8192:
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8183:
8178:
8175:
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8161:
8144:
8141:
8136:
8131:
8126:
8121:
8118:
8110:
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8048:
8045:
8037:
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8024:
8019:
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8004:
7999:
7970:
7967:
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7937:
7934:
7931:
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7922:
7918:
7915:
7912:
7907:
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7899:
7896:
7893:
7888:
7884:
7860:
7857:
7854:
7851:
7848:
7845:
7839:
7836:
7814:
7811:
7808:
7799:
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7786:
7780:
7776:
7772:
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7758:
7755:
7751:
7742:
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7724:
7721:
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7697:
7694:
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7639:
7633:
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7624:
7621:
7617:
7613:
7607:
7604:
7601:
7598:
7595:
7589:
7581:
7579:
7575:
7571:
7544:
7527:
7517:
7514:
7510:
7506:
7503:
7497:
7491:
7483:
7480:
7476:
7452:
7444:
7441:
7437:
7413:
7410:
7404:
7401:
7395:
7386:
7378:
7375:
7371:
7350:
7328:
7325:
7321:
7312:
7309:to represent
7296:
7288:
7285:
7281:
7266:
7258:
7255:
7251:
7248:
7229:
7221:
7218:
7214:
7210:
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7191:
7188:
7184:
7158:
7150:
7145:
7129:
7106:
7098:
7093:
7090:
7086:
7082:
7076:
7073:
7065:
7062:
7058:
7050:
7046:
7031:
7008:
7000:
6997:
6993:
6989:
6983:
6980:
6972:
6969:
6965:
6957:
6956:even function
6953:
6952:
6935:
6932:
6924:
6921:
6917:
6913:
6907:
6899:
6896:
6892:
6883:
6882:
6881:
6879:
6868:
6855:
6852:
6839:
6836:
6833:
6827:
6818:
6812:
6807:
6804:
6799:
6795:
6787:
6783:
6778:
6774:
6768:
6760:
6757:
6753:
6744:
6741:
6728:
6725:
6712:
6706:
6697:
6694:
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6685:
6680:
6677:
6672:
6668:
6660:
6656:
6651:
6647:
6641:
6633:
6630:
6626:
6617:
6603:
6580:
6577:
6572:
6568:
6564:
6559:
6555:
6508:
6488:
6468:
6454:
6452:
6448:
6443:
6440:
6423:
6411:
6408:
6405:
6399:
6389:
6383:
6378:
6375:
6372:
6367:
6364:
6361:
6357:
6351:
6348:
6335:
6327:
6325:
6317:
6309:
6306:
6302:
6294:
6274:
6268:
6259:
6256:
6253:
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6242:
6237:
6233:
6227:
6224:
6211:
6203:
6201:
6193:
6185:
6182:
6178:
6165:
6163:
6158:
6144:
6124:
6116:
6111:
6094:
6090:
6077:
6074:
6071:
6065:
6055:
6049:
6045:
6041:
6035:
6033:
6025:
6017:
6014:
6010:
6001:
5988:
5985:
5982:
5976:
5967:
5961:
5957:
5953:
5947:
5945:
5937:
5929:
5926:
5922:
5909:
5907:
5900:
5878:
5875:
5872:
5866:
5856:
5850:
5845:
5842:
5839:
5835:
5831:
5825:
5817:
5814:
5810:
5800:
5783:
5777:
5757:
5737:
5723:
5709:
5686:
5680:
5672:
5647:
5641:
5628:
5615:
5595:
5592:
5589:
5583:
5574:
5568:
5555:
5551:
5547:
5544:
5524:
5518:
5509:
5506:
5503:
5497:
5484:
5480:
5476:
5470:
5462:
5459:
5455:
5445:
5431:
5408:
5402:
5394:
5375:
5367:
5364:
5360:
5336:
5330:
5323:
5313:
5311:
5307:
5263:
5246:
5240:
5220:
5191:
5185:
5160:
5154:
5140:
5134:
5077:
5060:
5054:
5034:
5005:
4999:
4974:
4968:
4954:
4948:
4923:
4919:
4916:
4899:
4889:
4881:for all
4875:
4872:
4864:
4811:
4801:
4793:for all
4787:
4784:
4776:
4737:
4733:
4730:
4726:
4722:
4721:
4715:
4696:
4692:
4686:
4682:
4675:
4665:-th entry is
4649:
4646:
4643:
4633:matrix whose
4620:
4617:
4614:
4551:
4545:
4541:
4537:
4532:
4528:
4524:
4519:
4515:
4510:
4505:
4491:
4489:
4456:
4443:
4415:
4406:
4381:
4379:
4352:
4337:
4323:
4319:
4313:
4309:
4302:
4294:
4284:
4280:
4274:
4270:
4263:
4250:
4246:
4240:
4236:
4229:
4216:
4211:
4206:
4201:
4186:
4182:
4176:
4172:
4165:
4157:
4147:
4143:
4137:
4133:
4126:
4113:
4109:
4103:
4099:
4092:
4074:
4070:
4064:
4060:
4053:
4045:
4035:
4031:
4025:
4021:
4014:
4001:
3997:
3991:
3987:
3980:
3971:
3966:
3941:
3938:
3924:
3921:
3918:
3910:
3876:
3862:
3838:
3834:
3825:
3799:
3797:
3793:
3789:
3785:
3755:
3751:
3747:
3744:
3741:
3736:
3732:
3725:
3713:
3712:random vector
3708:
3706:
3668:
3665:
3662:
3628:
3624:
3620:
3617:
3614:
3609:
3605:
3598:
3586:
3585:random vector
3582:
3572:
3559:
3556:
3542:
3539:
3536:
3533:
3527:
3524:
3518:
3512:
3507:
3504:
3486:
3482:
3478:
3472:
3464:
3461:
3457:
3448:
3435:
3421:
3418:
3415:
3412:
3406:
3403:
3397:
3389:
3386:
3382:
3368:
3364:
3360:
3354:
3348:
3343:
3340:
3327:
3325:
3320:
3307:
3304:
3291:
3288:
3285:
3282:
3279:
3276:
3272:
3265:
3259:
3254:
3251:
3233:
3229:
3225:
3219:
3211:
3208:
3204:
3195:
3182:
3169:
3166:
3163:
3160:
3157:
3153:
3146:
3138:
3135:
3131:
3117:
3113:
3109:
3103:
3097:
3092:
3089:
3076:
3074:
3056:
3053:
3049:
3041:
3023:
3020:
3007:
2997:
2983:
2963:
2943:
2940:
2937:
2929:
2925:
2915:
2901:
2895:
2881:
2877:
2872:
2862:
2858:
2851:
2845:
2831:
2827:
2822:
2812:
2808:
2802:
2797:
2792:
2783:
2779:
2775:
2770:
2766:
2759:
2754:
2751:
2742:
2732:
2722:
2705:
2699:
2694:
2691:
2663:
2657:
2652:
2649:
2641:
2637:
2630:
2624:
2619:
2616:
2607:
2592:
2579:
2567:
2564:
2558:
2553:
2550:
2539:
2533:
2527:
2522:
2519:
2483:
2479:
2475:
2470:
2466:
2459:
2454:
2451:
2440:
2432:
2428:
2424:
2419:
2415:
2408:
2403:
2400:
2387:
2386:even function
2369:
2366:
2342:
2340:
2335:
2317:
2313:
2307:
2294:
2291:
2286:
2282:
2269:
2266:
2261:
2258:
2255:
2251:
2243:
2239:
2230:
2223:
2219:
2211:
2205:
2200:
2197:
2186:
2180:
2172:
2169:
2165:
2156:
2154:
2149:
2147:
2128:
2125:
2122:
2119:
2094:
2091:
2087:
2077:
2064:
2054:
2050:
2045:
2037:
2033:
2028:
2021:
2004:
2000:
1995:
1991:
1984:
1980:
1975:
1958:
1954:
1949:
1945:
1938:
1934:
1929:
1921:
1917:
1908:
1898:
1894:
1889:
1881:
1877:
1872:
1861:
1857:
1853:
1848:
1844:
1837:
1832:
1829:
1818:
1810:
1806:
1802:
1797:
1793:
1784:
1781:
1777:
1768:
1765:
1763:
1759:
1752:Normalization
1749:
1736:
1731:
1727:
1723:
1717:
1711:
1706:
1703:
1690:
1686:
1668:
1663:
1660:
1656:
1650:
1641:
1633:
1630:
1627:
1623:
1618:
1614:
1608:
1604:
1591:
1588:
1583:
1579:
1566:
1563:
1558:
1555:
1552:
1548:
1540:
1536:
1530:
1524:
1518:
1513:
1510:
1496:
1494:
1488:
1474:
1468:
1459:
1451:
1448:
1445:
1441:
1436:
1432:
1426:
1420:
1414:
1409:
1406:
1392:
1391:
1373:
1369:
1365:
1360:
1356:
1352:
1349:
1341:
1340:even function
1323:
1319:
1296:
1292:
1269:
1265:
1244:
1236:
1219:
1214:
1210:
1206:
1191:
1189:
1182:
1165:
1161:
1151:
1141:
1137:
1132:
1128:
1124:
1116:
1112:
1102:
1092:
1088:
1083:
1078:
1074:
1068:
1064:
1047:
1043:
1038:
1034:
1027:
1023:
1018:
1001:
997:
992:
988:
981:
977:
972:
964:
960:
954:
946:
942:
938:
933:
929:
922:
917:
914:
900:
884:
880:
857:
853:
844:
839:
837:
833:
829:
803:
789:
781:
777:
767:
757:
753:
748:
743:
739:
733:
725:
721:
717:
712:
708:
701:
696:
693:
679:
663:
659:
636:
632:
623:
607:
587:
565:
560:
556:
548:
530:
526:
518:
502:
494:
490:
472:
468:
459:
455:
452:process or a
451:
450:discrete-time
447:
431:
411:
390:
385:
381:
377:
368:
364:
360:
350:
348:
344:
340:
336:
332:
330:
325:
323:
319:
315:
311:
307:
303:
299:
295:
291:
288:case, is the
287:
286:discrete time
283:
279:
260:
257:
254:
234:
231:
228:
208:
204:
199:
192:
188:
183:
172:
167:
165:
160:
158:
153:
152:
150:
149:
142:
139:
137:
134:
132:
129:
127:
124:
123:
120:
115:
114:
107:
104:
102:
99:
97:
94:
92:
89:
88:
85:
80:
79:
72:
69:
67:
64:
62:
59:
57:
54:
53:
50:
45:
44:
40:
36:
35:
32:
29:
28:
25:
21:
20:
13474:
13462:
13443:
13436:
13348:Econometrics
13298: /
13281:Chemometrics
13258:Epidemiology
13251: /
13224:Applications
13066:ARIMA model
13043:
13013:Q-statistic
12962:Stationarity
12858:Multivariate
12801: /
12797: /
12795:Multivariate
12793: /
12733: /
12729: /
12503:Bayes factor
12402:Signed rank
12314:
12288:
12280:
12268:
11963:Completeness
11799:Cohort study
11697:Opinion poll
11632:Missing data
11619:Study design
11574:Scatter plot
11496:Scatter plot
11489:Spearman's Ï
11451:Grouped data
11151:
11126:
11091:
11087:
11063:
11034:
11007:. Retrieved
10986:
10978:the original
10971:
10961:
10936:
10932:
10925:
10906:
10900:
10857:
10853:
10843:
10800:
10796:
10786:
10767:
10761:
10752:
10743:
10726:
10722:
10716:
10691:
10683:
10664:
10658:
10615:
10610:
10604:
10585:
10579:
10560:
10554:
10535:
10529:
10510:
10493:
10437:
10187:
10132:
10123:
10122:
10054:astrophysics
10039:mass spectra
10010:musical beat
9905:produced by
9878:
9875:Applications
9728:
9722:
9711:
9706:
9668:
9664:
9660:
9652:
9638:
9618:econometrics
9607:
9576:
9528:
9306:
9245:
9170:
9017:
8922:
8910:
8906:
8900:data with a
8895:
8891:
8880:
8869:
8680:
8669:
8665:
8654:
8650:
8644:
8638:
8162:
7730:
7722:
7582:
7567:
6874:
6745:
6742:
6618:
6460:
6447:last forever
6446:
6444:
6441:
6166:
6159:
6112:
5910:
5902:
5802:
5729:
5630:
5447:
5395:integral of
5319:
5309:
5303:
4921:
4492:
4457:
4382:
4353:
3942:
3939:
3907:denotes the
3878:
3801:
3795:
3709:
3707:algorithms.
3580:
3578:
3449:
3328:
3321:
3196:
3077:
3003:
2921:
2728:
2679:Notice that
2598:
2353:
2336:
2157:
2150:
2078:
1769:
1766:
1755:
1691:
1688:
1498:
1492:
1490:
1394:
1389:
1342:of the lag
1197:
1184:
902:
842:
840:
836:well defined
805:
681:
621:
356:
333:
326:
304:obscured by
281:
277:
276:
206:
118:
83:
48:
13476:WikiProject
13391:Cartography
13353:Jurimetrics
13305:Reliability
13036:Time domain
13015:(LjungâBox)
12937:Time-series
12815:Categorical
12799:Time-series
12791:Categorical
12726:(Bernoulli)
12561:Correlation
12541:Correlation
12337:JarqueâBera
12309:Chi-squared
12071:M-estimator
12024:Asymptotics
11968:Sufficiency
11735:Interaction
11647:Replication
11627:Effect size
11584:Violin plot
11564:Radar chart
11544:Forest plot
11534:Correlogram
11484:Kendall's Ï
11094:(5): 2180.
11029:Kmenta, Jan
10854:Soft Matter
10347:Correlogram
10135:time series
10083:geosciences
9933:calculated.
9316:periodogram
8902:logarithmic
8634:Z-transform
7570:dimensional
7311:convolution
3794:exist, the
3782:containing
2924:white noise
600:, for each
489:realization
454:real number
337:processes,
322:time domain
290:correlation
191:correlogram
13492:Categories
13343:Demography
13061:ARMA model
12866:Regression
12443:(Friedman)
12404:(Wilcoxon)
12342:Normality
12332:Lilliefors
12279:Student's
12155:Resampling
12029:Robustness
12017:divergence
12007:Efficiency
11945:(monotone)
11940:Likelihood
11857:Population
11690:Stratified
11642:Population
11461:Dependence
11417:Count data
11348:Percentile
11325:Dispersion
11258:Arithmetic
11193:Statistics
11116:Guang Gong
10939:: 106173.
10410:References
10225:stationary
10087:geophysics
10069:panel data
10006:distortion
9731:, we have
8919:Estimation
6871:Properties
6596:of length
6115:stationary
3909:transposed
2345:Properties
444:may be an
359:statistics
24:Statistics
12724:Logistic
12491:posterior
12417:Rank sum
12165:Jackknife
12160:Bootstrap
11978:Bootstrap
11913:Parameter
11862:Statistic
11657:Statistic
11569:Run chart
11554:Pie chart
11549:Histogram
11539:Fan chart
11514:Bar chart
11396:L-moments
11283:Geometric
11153:MathWorld
11067:. Wiley.
10953:198468676
10884:1744-683X
10625:0912.3824
10290:−
10281:τ
9987:frequency
9983:astronomy
9853:τ
9824:τ
9792:…
9774:τ
9751:≠
9745:τ
9686:χ
9496:…
9425:−
9410:…
9329:−
9287:σ
9266:μ
9226:σ
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9154:μ
9151:−
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9123:−
9102:−
9084:∑
9071:σ
9061:−
9031:^
8986:…
8834:
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8794:∗
8721:
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8594:…
8552:…
8503:…
8494:−
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8419:−
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8217:−
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8119:−
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8081:−
8054:−
8046:−
8035:−
8020:×
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7935:−
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7812:−
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7701:−
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7618:∑
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7580:would be
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7507:∗
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7411:−
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7211:≤
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7099:∗
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7074:−
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6075:−
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5836:∑
5826:ℓ
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5000:−
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4230:
4217:⋮
4212:⋱
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2809:
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2206:
2181:τ
2166:ρ
2120:−
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2046:σ
2029:σ
2016:¯
1996:μ
1992:−
1950:μ
1946:−
1918:
1890:σ
1873:σ
1838:
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771:¯
740:
702:
557:σ
527:μ
335:Unit root
324:signals.
258:⋆
232:∗
13438:Category
13131:Survival
13008:Johansen
12731:Binomial
12686:Isotonic
12273:(normal)
11918:location
11725:Blocking
11680:Sampling
11559:QâQ plot
11524:Box plot
11506:Graphics
11401:Skewness
11391:Kurtosis
11363:Variance
11293:Heronian
11288:Harmonic
11031:(1986).
11000:Archived
10892:28106203
10835:22208184
10309:See also
10058:galaxies
9926:micelles
9716:and the
9663:, where
9634:t-scores
9589:(AR), a
9252:variance
9247:unbiased
8925:discrete
8235:, where
7733:discrete
5320:Given a
4486:denotes
3792:variance
3071:via the
1491:and the
580:at time
547:variance
314:harmonic
13464:Commons
13411:Kriging
13296:Process
13253:studies
13112:Wavelet
12945:General
12112:Plug-in
11906:L space
11685:Cluster
11386:Moments
11204:Outline
11096:Bibcode
11041:298â334
10862:Bibcode
10826:3244056
10805:Bibcode
10650:7173093
10630:Bibcode
10047:peptide
10035:SEQUEST
9991:pulsars
9671:is the
8678:(FFT):
6162:ergodic
5750:at lag
4738:, i.e.
3038:to the
826:is the
446:integer
365:is the
284:in the
13333:Census
12923:Normal
12871:Manova
12691:Robust
12441:2-way
12433:1-way
12271:-test
11942:
11519:Biplot
11310:Median
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11245:Center
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7568:Multi-
5631:where
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456:for a
448:for a
345:, and
294:signal
205:, and
12957:Trend
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12428:anova
12317:-test
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12283:-test
12190:Power
12135:Pivot
11928:shape
11923:scale
11373:Shape
11353:Range
11298:Heinz
11273:Cubic
11209:Index
11003:(PDF)
10996:(PDF)
10949:S2CID
10646:S2CID
10620:arXiv
10357:CUSUM
10137:of a
10014:tempo
9998:music
9900:light
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292:of a
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11315:Mode
11253:Mean
11133:ISBN
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11045:ISBN
11011:2022
10973:Time
10911:ISBN
10888:PMID
10880:ISSN
10831:PMID
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2729:The
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872:and
651:and
545:and
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247:and
187:sine
12370:BIC
12365:AIC
11104:doi
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1737:.
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