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7704:
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459:
assesses the stability of IMF and trend components. For stationary time series, the
Autoregressive Moving Average (ARMA) model is used, while for non-stationary series, LSTM models are employed to derive abstract features. The final value is obtained by reconstructing the predicted outcomes of each
3097:
2307:
Unlike other methods of regression (i.e. OLS, 2SLS, etc.) often employed in econometric analysis, ARMA model outputs are used primarily for the cases of forecasting time-series data. Their coefficients are then as such only utilized for prediction. Other areas of econometrics look at the causal
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2661:
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ARMA is appropriate when a system is a function of a series of unobserved shocks (the MA or moving average part) as well as its own behavior. For example, stock prices may be shocked by fundamental information as well as exhibiting technical trending and
2809:(ARIMA) models. If multiple time series are to be fitted then a vector ARIMA (or VARIMA) model may be fitted. If the time-series in question exhibits long memory then fractional ARIMA (FARIMA, sometimes called ARFIMA) modelling may be appropriate: see
2187:
1096:
3191:
Statistical packages implement the ARMAX model through the use of "exogenous" (that is, independent,) variables. Care must be taken when interpreting the output of those packages, because the estimated parameters usually (for example, in
2508:
is a Java library of numerical methods, including comprehensive statistics packages, in which univariate/multivariate ARMA, ARIMA, ARMAX, etc. models are implemented in an object-oriented approach. These implementations are documented in
580:
2245:. Extended autocorrelation functions (EACF) can be used to simultaneously determine p and q. Further information can be gleaned by considering the same functions for the residuals of a model fitted with an initial selection of
2908:
115:, the ARMA model is a tool for understanding and, perhaps, predicting future values in this series. The AR part involves regressing the variable on its own lagged (i.e., past) values. The MA part involves modeling the
1799:& Reinsel use a different convention for the autoregression coefficients. This allows all the polynomials involving the lag operator to appear in a similar form throughout. Thus the ARMA model would be written as
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263:
1205:
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1805:
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782:
1220:
3146:
635:
409:
742:
2061:
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709:
343:
978:
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2023:
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are libraries of numerical analysis functionality including ARMA and ARIMA procedures implemented in standard programming languages like C, Java, C# .NET, and
Fortran.
1119:
2712:
1370:
3413:
3179:
2900:
2780:
2732:
682:
113:
4202:
655:
350:
1987:
17:
488:
2810:
4108:
Francq, C.; ZakoĂŻan, J.-M. (2005), "Recent results for linear time series models with non independent innovations", in
Duchesne, P.; Remillard, B. (eds.),
3092:{\displaystyle X_{t}=\varepsilon _{t}+\sum _{i=1}^{p}\varphi _{i}X_{t-i}+\sum _{i=1}^{q}\theta _{i}\varepsilon _{t-i}+\sum _{i=1}^{b}\eta _{i}d_{t-i}.\,}
2292:
regression to find the values of the parameters which minimize the error term. It is generally considered good practice to find the smallest values of
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5164:
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178:
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4694:
4674:
2820:(MAR) model. A MAR model is indexed by the nodes of a tree, whereas a standard (discrete time) autoregressive model is indexed by integers.
2802:
2471:
7480:
5078:
3378:{\displaystyle X_{t}-m_{t}=\varepsilon _{t}+\sum _{i=1}^{p}\varphi _{i}(X_{t-i}-m_{t-i})+\sum _{i=1}^{q}\theta _{i}\varepsilon _{t-i}.\,}
7104:
5745:
1127:
1623:{\displaystyle \left(1-\sum _{i=1}^{p}\varphi _{i}L^{i}\right)X_{t}=\left(1+\sum _{i=1}^{q}\theta _{i}L^{i}\right)\varepsilon _{t}\,,}
4995:
2505:
1378:
2520:
2308:
inference, time-series forecasting using ARMA is not. The coefficients should then only be seen as useful for predictive modelling.
6878:
4679:
3514:
3185:
2806:
2495:
2455:
1953:{\displaystyle \left(1-\sum _{i=1}^{p}\phi _{i}L^{i}\right)X_{t}=\left(1+\sum _{i=1}^{q}\theta _{i}L^{i}\right)\varepsilon _{t}\,.}
1639:
7317:
5005:
4689:
3421:
2813:. If the data is thought to contain seasonal effects, it may be modeled by a SARIMA (seasonal ARIMA) or a periodic ARMA model.
5047:
4944:
5234:
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Statsmodels Python module includes many models and functions for time series analysis, including ARMA. Formerly part of the
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5098:
123:
of error terms occurring contemporaneously and at various times in the past. The model is usually referred to as the ARMA(
6344:
5492:
5402:
5139:
916:{\displaystyle X_{t}=\varepsilon _{t}+\sum _{i=1}^{p}\varphi _{i}X_{t-i}+\sum _{i=1}^{q}\theta _{i}\varepsilon _{t-i}.\,}
5051:
4249:
4150:
3917:
2786:
is assumed to be linear unless specified otherwise. If the dependence is nonlinear, the model is specifically called a
1342:{\displaystyle X_{t}-\mu =\left(1+\sum _{i=1}^{q}\theta _{i}L^{i}\right)\varepsilon _{t}=\theta (L)\varepsilon _{t},\,}
946:) method for choosing and estimating them. This method was useful for low-order polynomials (of degree three or less).
271:
116:
2656:{\displaystyle S(f)={\frac {\sigma ^{2}}{2\pi }}\left\vert {\frac {\theta (e^{-if})}{\phi (e^{-if})}}\right\vert ^{2}}
2200:, the ARMA model is represented as a digital filter with white noise at the input and the ARMA process at the output.
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4023:
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to simulate data from these models. Extension packages contain related and extended functionality, e.g., the
927:
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58:
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7208:
7157:
7142:
7132:
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6666:
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6451:
5189:
3628:. Gwilym M. Jenkins, Gregory C. Reinsel (3rd ed.). Englewood Cliffs, N.J.: Prentice Hall. p. 54.
2428:
2257:
5194:
4830:
2182:{\displaystyle -\sum _{i=0}^{p}\phi _{i}L^{i}\;X_{t}=\sum _{i=0}^{q}\theta _{i}L^{i}\;\varepsilon _{t}\,.}
371:
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1091:{\displaystyle \varepsilon _{t}=\left(1-\sum _{i=1}^{p}\varphi _{i}L^{i}\right)X_{t}=\varphi (L)X_{t}\,}
714:
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Some nonlinear variants of models with exogenous variables have been defined: see for example
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31:
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4126:
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3157:
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2758:
2717:
2334:
660:
469:
155:
91:
640:
575:{\displaystyle X_{t}=\mu +\varepsilon _{t}+\sum _{i=1}^{q}\theta _{i}\varepsilon _{t-i}\,}
8:
7694:
7619:
7542:
7223:
6987:
6980:
6942:
6850:
6830:
6802:
6535:
6401:
6396:
6386:
6378:
6196:
6157:
6047:
6037:
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5681:
5599:
5524:
5426:
5379:
5219:
5144:
4949:
4709:
4619:
4509:
3880:. Wiley series in probability and mathematical statistics. New York: John Wiley and Sons.
3873:
3804:. Wiley series in probability and mathematical statistics. New York: John Wiley and Sons.
3797:
2422:
1966:
744:,... are again i.i.d. white noise error terms that are commonly normal random variables.
354:
7708:
7519:
7373:
7269:
7218:
7094:
6991:
6975:
6952:
6729:
6463:
6446:
6406:
6317:
6212:
6174:
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5928:
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5609:
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4624:
4289:
4227:
4166:
4068:
2384:
361:
120:
3733:(5th ed.). Hoboken, New Jersey: John Wiley & Sons, Incorporated. p. 53.
7703:
7614:
7584:
7576:
7396:
7387:
7312:
7243:
7099:
7084:
7059:
6947:
6888:
6754:
6742:
6368:
6285:
6229:
6152:
5996:
5918:
5697:
5571:
5369:
4582:
4499:
4468:
4361:
4341:
4331:
4187:
4182:
4094:
4075:
4029:
4019:
3994:
3984:
3939:
3896:
3847:
3827:
3779:
3769:
3744:
3734:
3709:
3699:
3674:
3664:
3639:
3629:
2458:
has a Python-based implementation of ARIMAX models, including
Bayesian ARIMAX models.
2445:
2431:
has some community driven packages that implement fitting with an ARMA model such as
2400:
1796:
5174:
4825:
3727:
Box, George E. P.; Jenkins, Gwilym M.; Reinsel, Gregory C.; Ljung, Greta M. (2016).
368:
must lie outside of the unit circle. For example, processes in the AR(1) model with
7639:
7594:
7358:
7345:
7238:
7213:
7147:
7079:
6957:
6565:
6458:
6391:
6304:
6251:
6070:
5941:
5735:
5619:
5534:
5501:
5389:
5276:
5159:
5035:
4772:
4529:
4504:
4453:
4304:
4257:
2714:
is the characteristic polynomial of the moving average part of the ARMA model, and
2533:
2412:
2358:
939:
935:
78:
4381:
2510:
2406:
7556:
7300:
7162:
7089:
6764:
6638:
6611:
6588:
6557:
6184:
6179:
6133:
5863:
5514:
5354:
5254:
5239:
5000:
4934:
4612:
4556:
4539:
4284:
3965:
953:
filter applied to white noise, with some additional interpretation placed on it.
943:
7046:
5169:
4401:
2801:
Autoregressiveâmoving-average models can be generalized in other ways. See also
7505:
7500:
5963:
5893:
5539:
5359:
5324:
5244:
4850:
4597:
4514:
4483:
4478:
4458:
4448:
4391:
4366:
4346:
4311:
4279:
4262:
2734:
is the characteristic polynomial of the autoregressive part of the ARMA model.
2516:
931:
82:
4386:
7748:
7662:
7629:
7492:
7453:
7264:
7233:
6697:
6651:
6256:
5958:
5785:
5549:
5544:
5261:
4802:
4634:
4592:
4534:
4356:
4272:
4212:
3748:
2835:
Autoregressiveâmoving-average model with exogenous inputs model (ARMAX model)
2289:
4033:
3998:
3783:
3713:
3678:
3643:
938:) and statistical inference. ARMA models were popularized by a 1970 book by
7604:
7537:
7514:
7429:
6759:
6055:
5953:
5888:
5830:
5815:
5752:
5707:
5319:
5281:
4835:
4767:
4656:
4651:
4463:
4396:
4371:
4207:
2441:
962:
3728:
1776:{\displaystyle {\frac {\varphi (L)}{\theta (L)}}X_{t}=\varepsilon _{t}\,.}
7647:
7609:
7292:
7193:
7055:
6868:
6835:
6327:
6244:
6239:
5883:
5840:
5820:
5800:
5790:
5559:
5364:
4899:
4883:
4878:
4873:
4863:
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4602:
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4326:
4217:
4013:
3978:
3763:
3693:
3658:
3623:
2390:
346:
258:{\displaystyle X_{t}=\sum _{i=1}^{p}\varphi _{i}X_{t-i}+\varepsilon _{t}}
42:
2499:
2417:
to estimate AR, ARX (autoregressive exogenous), and ARMAX models. See
6493:
5973:
5673:
5604:
5554:
5529:
5449:
5374:
4914:
4858:
4742:
4695:
Generalized autoregressive conditional heteroskedasticity (GARCH) model
4135:
3698:(3rd ed.). Englewood Cliffs, N.J.: Prentice Hall. pp. 54â55.
2477:
2432:
1792:
38:
2449:
2300:
which provide an acceptable fit to the data. For a pure AR model the
6646:
6498:
6118:
5913:
5825:
5810:
5805:
5770:
4868:
315:
6162:
5780:
5657:
5652:
5647:
3692:
Box, George E. P.; Jenkins, Gwilym M.; Reinsel, Gregory C. (1994).
2691:
66:
62:
7667:
7368:
2481:
1200:{\displaystyle \varphi (L)=1-\sum _{i=1}^{p}\varphi _{i}L^{i}.\,}
69:(MA). The general ARMA model was described in the 1951 thesis of
7589:
6570:
6544:
6524:
5775:
5566:
4015:
Time series analysis : univariate and multivariate methods
2396:
2393:
has a complete library of time series functions including ARMA.
1451:{\displaystyle \theta (L)=1+\sum _{i=1}^{q}\theta _{i}L^{i}.\,}
4018:. Redwood City, Calif.: Addison-Wesley Pub. pp. 242â243.
3980:
Gaussian and non-Gaussian linear time series and random fields
2519:
has an econometric package, ETS, that estimates ARIMA models.
2480:
can estimate AR models using functions from the extra package
2341:
for fitting ARMA models (seasonal and nonseasonal) as well as
5418:
3891:
Box, George; Jenkins, Gwilym M.; Reinsel, Gregory C. (1994).
3197:
2487:
2467:
1694:{\displaystyle \varphi (L)X_{t}=\theta (L)\varepsilon _{t}\,}
5509:
4110:
Statistical
Modeling and Analysis for Complex Data Problems
961:
In some texts the models will be specified in terms of the
926:
The general ARMA model was described in the 1951 thesis of
4675:
Autoregressive conditional heteroskedasticity (ARCH) model
3498:{\displaystyle m_{t}=c+\sum _{i=0}^{b}\eta _{i}d_{t-i}.\,}
4129:
Time Series
Analysis and Its Applications with R Examples
2311:
956:
4203:
Independent and identically distributed random variables
3844:
Prediction and
Regulation by Linear Least-Square Methods
3663:. David S. Stoffer. New York: Springer. pp. 90â91.
2831:(VAR) and Vector Autoregression Moving-Average (VARMA).
2444:
library, it is now stand-alone and integrates well with
3415:
incorporates all exogenous (or independent) variables:
2268:. Another possible choice for order determining is the
4680:
Autoregressive integrated moving average (ARIMA) model
3726:
3915:
3424:
3394:
3209:
3160:
3108:
2911:
2881:
2811:
Autoregressive fractionally integrated moving average
2761:
2720:
2700:
2669:
2542:
2064:
2031:
1995:
1969:
1808:
1713:
1642:
1478:
1381:
1358:
1223:
1130:
1107:
981:
785:
717:
690:
663:
643:
591:
491:
417:
374:
324:
274:
181:
94:
7331:
Autoregressive conditional heteroskedasticity (ARCH)
3768:. David S. Stoffer. New York: Springer. p. 98.
2827:
model. Extensions for the multivariate case are the
2368:
for fractionally integrated ARMA processes; and the
3730:
Time series analysis : forecasting and control
3695:
Time series analysis : forecasting and control
3625:
Time series analysis : forecasting and control
2863:
exogenous inputs terms. This model contains the AR(
2511:"SuanShu, a Java numerical and statistical library"
6793:
4067:
3497:
3407:
3377:
3173:
3140:
3091:
2894:
2774:
2726:
2706:
2682:
2655:
2181:
2050:
2017:
1981:
1952:
1775:
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1622:
1450:
1364:
1341:
1199:
1113:
1090:
915:
736:
703:
676:
649:
629:
574:
445:
403:
337:
306:
257:
107:
3938:(2nd ed.). New York: Springer. p. 273.
3890:
3691:
768:moving-average terms. This model contains the AR(
307:{\displaystyle \varphi _{1},\ldots ,\varphi _{p}}
30:"ARMA model" redirects here. For other uses, see
7746:
4562:Stochastic chains with memory of variable length
2058:, then we get an even more elegant formulation:
139:is the order of the MA part (as defined below).
6879:Multivariate adaptive regression splines (MARS)
4089:Percival, Donald B.; Walden, Andrew T. (1993).
4088:
3933:
3872:
3868:
2871:) models and a linear combination of the last
2280:ARMA models in general can be, after choosing
478:) refers to the moving average model of order
164:) refers to the autoregressive model of order
27:Statistical model used in time series analysis
5434:
4151:
4107:
4040:
3893:Time Series Analysis: Forecasting and Control
2803:autoregressive conditional heteroskedasticity
2191:
77:, and it was popularized in the 1970 book by
4091:Spectral Analysis for Physical Applications
3918:"Model Specification, Time Series Analysis"
3841:
3821:
3814:
3141:{\displaystyle \eta _{1},\ldots ,\eta _{b}}
2229:) model can be facilitated by plotting the
630:{\displaystyle \theta _{1},...,\theta _{q}}
5479:
5441:
5427:
4690:Autoregressiveâmoving-average (ARMA) model
4158:
4144:
4131:. Springer. DOI: 10.1007/978-3-319-52452-8
3976:
3817:Hypothesis Testing in Time Series Analysis
2875:terms of a known and external time series
2275:
2164:
2109:
142:ARMA models can be estimated by using the
75:Hypothesis testing in time series analysis
6092:
4117:
3765:Time series analysis and its applications
3660:Time series analysis and its applications
3596:Learn how and when to remove this message
3494:
3374:
3088:
2175:
1946:
1769:
1690:
1616:
1447:
1338:
1196:
1087:
942:and Jenkins, who expounded an iterative (
912:
571:
61:in terms of two polynomials, one for the
4165:
4127:Shumway, R.H. and Stoffer, D.S. (2017).
3559:This article includes a list of general
3515:Autoregressive integrated moving average
3186:Nonlinear autoregressive exogenous model
2807:autoregressive integrated moving average
57:provide a parsimonious description of a
3934:Brockwell, P. J.; Davis, R. A. (2009).
3761:
3656:
2796:nonlinear autoregressiveâmoving-average
1786:
463:
411:are not stationary because the root of
351:independent and identically distributed
149:
14:
7747:
7405:KaplanâMeier estimator (product limit)
4996:Doob's martingale convergence theorems
3796:
2312:Implementations in statistics packages
2256:Brockwell & Davis recommend using
957:Specification in terms of lag operator
59:(weakly) stationary stochastic process
7478:
7045:
6792:
6091:
5861:
5478:
5422:
4748:Constant elasticity of variance (CEV)
4738:ChanâKarolyiâLongstaffâSanders (CKLS)
4139:
4070:Time Series Techniques for Economists
4065:
7715:
7415:Accelerated failure time (AFT) model
3878:Statistical theory of linear systems
3545:
2782:on past values and the error terms Δ
2747:effects due to market participants.
2379:for selecting a parsimonious set of
1963:Moreover, starting summations from
684:(often assumed to equal 0), and the
404:{\displaystyle |\varphi _{1}|\geq 1}
7727:
7010:Analysis of variance (ANOVA, anova)
5862:
4011:
3959:Time series features in Mathematica
3621:
2208:
24:
18:Autoregressiveâmoving-average model
7105:CochranâMantelâHaenszel statistics
5731:Pearson product-moment correlation
5235:Skorokhod's representation theorem
5016:Law of large numbers (weak/strong)
4059:
3983:. New York: Springer. p. 10.
3565:it lacks sufficient corresponding
2750:
930:, who used mathematical analysis (
737:{\displaystyle \varepsilon _{t-1}}
25:
7766:
5205:Martingale representation theorem
3895:(Third ed.). Prentice-Hall.
3846:. University of Minnesota Press.
2231:partial autocorrelation functions
2203:
949:The ARMA model is essentially an
637:are the parameters of the model,
446:{\displaystyle 1-\varphi _{1}B=0}
360:In order for the model to remain
7726:
7714:
7702:
7689:
7688:
7479:
5250:Stochastic differential equation
5140:Doob's optional stopping theorem
5135:DoobâMeyer decomposition theorem
3550:
2387:contains links to most of these.
2355:"Fit ARMA Models to Time Series"
704:{\displaystyle \varepsilon _{t}}
338:{\displaystyle \varepsilon _{t}}
135:is the order of the AR part and
7364:Least-squares spectral analysis
5120:Convergence of random variables
5006:FisherâTippettâGnedenko theorem
4005:
3970:
3952:
3936:Time Series: Theory and Methods
3927:
3909:
2737:
6345:Mean-unbiased minimum-variance
5448:
4718:Binomial options pricing model
4112:, Springer, pp. 241â265,
4093:. Cambridge University Press.
4074:. Cambridge University Press.
4047:ARIMA Modelling of Time Series
3884:
3862:
3826:. English Universities Press.
3808:
3790:
3755:
3720:
3685:
3650:
3615:
3318:
3280:
2823:Note that the ARMA model is a
2816:Another generalization is the
2637:
2618:
2610:
2591:
2552:
2546:
2470:can also estimate ARMA model,
2337:has an improved script called
2331:ARIMA Modelling of Time Series
2325:function (in standard package
2304:may be used to provide a fit.
2213:Finding appropriate values of
1740:
1734:
1726:
1720:
1677:
1671:
1652:
1646:
1391:
1385:
1322:
1316:
1140:
1134:
1074:
1068:
391:
376:
13:
1:
7658:Geographic information system
6874:Simultaneous equations models
5185:Kolmogorov continuity theorem
5021:Law of the iterated logarithm
3608:
2472:see here where it's mentioned
2419:System Identification Toolbox
2051:{\displaystyle \theta _{0}=1}
968:. In these terms then the AR(
747:
453:lies within the unit circle.
47:autoregressiveâmoving-average
6841:Coefficient of determination
6452:Uniformly most powerful test
5190:Kolmogorov extension theorem
4869:Generalized queueing network
4377:Interacting particle systems
3876:; Deistler, Manfred (1988).
2494:which can estimate ARMA and
2258:Akaike information criterion
2018:{\displaystyle \phi _{0}=-1}
88:Given a time series of data
65:(AR) and the second for the
7:
7410:Proportional hazards models
7354:Spectral density estimation
7336:Vector autoregression (VAR)
6770:Maximum posterior estimator
6002:Randomized controlled trial
4322:Continuous-time random walk
4012:Wei, William W. S. (1990).
3977:Rosenblatt, Murray (2000).
3916:Missouri State University.
3869:Hannan & Deistler (1988
3762:Shumway, Robert H. (2000).
3657:Shumway, Robert H. (2000).
3508:
3200:) refer to the regression:
2851:) refers to the model with
2683:{\displaystyle \sigma ^{2}}
2527:
2399:includes functions such as
1461:Finally, the combined ARMA(
760:) refers to the model with
10:
7771:
7170:Multivariate distributions
5590:Average absolute deviation
5330:Extreme value theory (EVT)
5130:Doob decomposition theorem
4422:OrnsteinâUhlenbeck process
4193:Chinese restaurant process
4066:Mills, Terence C. (1990).
3964:November 24, 2011, at the
3622:Box, George E. P. (1994).
2192:Alternative interpretation
1372:represents the polynomial
1121:represents the polynomial
467:
153:
29:
7684:
7638:
7575:
7528:
7491:
7487:
7474:
7446:
7428:
7395:
7386:
7344:
7291:
7252:
7201:
7192:
7158:Structural equation model
7113:
7070:
7066:
7041:
7000:
6966:
6920:
6887:
6849:
6816:
6812:
6788:
6728:
6637:
6556:
6520:
6511:
6494:Score/Lagrange multiplier
6479:
6432:
6377:
6303:
6294:
6104:
6100:
6087:
6046:
6020:
5972:
5927:
5909:Sample size determination
5874:
5870:
5857:
5761:
5716:
5690:
5672:
5628:
5580:
5500:
5491:
5487:
5474:
5456:
5398:
5302:
5210:Optional stopping theorem
5107:
5069:
5011:Large deviation principle
4978:
4892:
4849:
4816:
4763:HeathâJarrowâMorton (HJM)
4708:
4700:Moving-average (MA) model
4685:Autoregressive (AR) model
4665:
4575:
4510:Hidden Markov model (HMM)
4492:
4444:SchrammâLoewner evolution
4248:
4173:
3824:Prediction and Regulation
3536:Infinite impulse response
2859:moving average terms and
2818:multiscale autoregressive
2521:See here for more details
2500:See here for more details
2450:See here for more details
2383:. The CRAN task view on
2239:autocorrelation functions
2237:, and likewise using the
2198:digital signal processing
951:infinite impulse response
764:autoregressive terms and
366:characteristic polynomial
7653:Environmental statistics
7175:Elliptical distributions
6968:Generalized linear model
6897:Simple linear regression
6667:HodgesâLehmann estimator
6124:Probability distribution
6033:Stochastic approximation
5595:Coefficient of variation
5125:Doléans-Dade exponential
4955:Progressively measurable
4753:CoxâIngersollâRoss (CIR)
3819:. Almquist and Wicksell.
3526:Linear predictive coding
2792:nonlinear autoregressive
2788:nonlinear moving average
2462:IMSL Numerical Libraries
2353:function, documented in
1791:Some authors, including
1114:{\displaystyle \varphi }
318:and the random variable
7313:Cross-correlation (XCF)
6921:Non-standard predictors
6355:LehmannâScheffĂ© theorem
6028:Adaptive clinical trial
5345:Mathematical statistics
5335:Large deviations theory
5165:Infinitesimal generator
5026:Maximal ergodic theorem
4945:Piecewise-deterministic
4547:Random dynamical system
4412:Markov additive process
3580:more precise citations.
3541:Finite impulse response
3154:of the exogenous input
2707:{\displaystyle \theta }
2276:Estimating coefficients
1365:{\displaystyle \theta }
355:normal random variables
7709:Mathematics portal
7530:Engineering statistics
7438:NelsonâAalen estimator
7015:Analysis of covariance
6902:Ordinary least squares
6826:Pearson product-moment
6230:Statistical functional
6141:Empirical distribution
5974:Controlled experiments
5703:Frequency distribution
5481:Descriptive statistics
5180:KarhunenâLoĂšve theorem
5115:CameronâMartin formula
5079:BurkholderâDavisâGundy
4474:Variance gamma process
3499:
3464:
3409:
3379:
3344:
3269:
3175:
3142:
3093:
3058:
3008:
2958:
2896:
2855:autoregressive terms,
2776:
2728:
2708:
2684:
2657:
2490:includes the function
2183:
2143:
2088:
2052:
2019:
1983:
1954:
1910:
1840:
1777:
1695:
1624:
1580:
1510:
1452:
1423:
1366:
1343:
1274:
1201:
1172:
1115:
1092:
1026:
917:
882:
832:
738:
705:
678:
657:is the expectation of
651:
631:
576:
544:
447:
405:
339:
308:
259:
215:
172:) model is written as
109:
7625:Population statistics
7567:System identification
7301:Autocorrelation (ACF)
7229:Exponential smoothing
7143:Discriminant analysis
7138:Canonical correlation
7002:Partition of variance
6864:Regression validation
6708:(JonckheereâTerpstra)
6607:Likelihood-ratio test
6296:Frequentist inference
6208:Locationâscale family
6129:Sampling distribution
6094:Statistical inference
6061:Cross-sectional study
6048:Observational studies
6007:Randomized experiment
5836:Stem-and-leaf display
5638:Central limit theorem
5310:Actuarial mathematics
5272:Uniform integrability
5267:Stratonovich integral
5195:LĂ©vyâProkhorov metric
5099:MarcinkiewiczâZygmund
4986:Central limit theorem
4588:Gaussian random field
4417:McKeanâVlasov process
4337:Dyson Brownian motion
4198:GaltonâWatson process
3521:Exponential smoothing
3500:
3444:
3410:
3408:{\displaystyle m_{t}}
3380:
3324:
3249:
3176:
3174:{\displaystyle d_{t}}
3143:
3094:
3038:
2988:
2938:
2897:
2895:{\displaystyle d_{t}}
2829:vector autoregression
2777:
2775:{\displaystyle X_{t}}
2729:
2727:{\displaystyle \phi }
2709:
2685:
2658:
2536:of an ARMA process is
2425:for more information.
2302:Yule-Walker equations
2184:
2123:
2068:
2053:
2020:
1984:
1955:
1890:
1820:
1778:
1696:
1625:
1560:
1490:
1453:
1403:
1367:
1344:
1254:
1202:
1152:
1116:
1093:
1006:
918:
862:
812:
739:
706:
679:
677:{\displaystyle X_{t}}
652:
632:
577:
524:
448:
406:
340:
309:
260:
195:
110:
108:{\displaystyle X_{t}}
32:ARMA (disambiguation)
7548:Probabilistic design
7133:Principal components
6976:Exponential families
6928:Nonlinear regression
6907:General linear model
6869:Mixed effects models
6859:Errors and residuals
6836:Confounding variable
6738:Bayesian probability
6716:Van der Waerden test
6706:Ordered alternative
6471:Multiple comparisons
6350:RaoâBlackwellization
6313:Estimating equations
6269:Statistical distance
5987:Factorial experiment
5520:Arithmetic-Geometric
5385:Time series analysis
5340:Mathematical finance
5225:Reflection principle
4552:Regenerative process
4352:FlemingâViot process
4167:Stochastic processes
3842:Whittle, P. (1983).
3822:Whittle, P. (1963).
3815:Whittle, P. (1951).
3802:Multiple time series
3798:Hannan, Edward James
3531:Predictive analytics
3422:
3392:
3207:
3158:
3106:
2909:
2879:
2759:
2718:
2698:
2694:of the white noise,
2667:
2540:
2423:Econometrics Toolbox
2349:package includes an
2062:
2029:
1993:
1967:
1806:
1787:Alternative notation
1711:
1640:
1476:
1469:) model is given by
1379:
1356:
1221:
1214:) model is given by
1128:
1105:
979:
972:) model is given by
783:
715:
688:
661:
650:{\displaystyle \mu }
641:
589:
489:
470:Moving-average model
464:Moving-average model
415:
372:
322:
272:
179:
156:Autoregressive model
150:Autoregressive model
92:
7620:Official statistics
7543:Methods engineering
7224:Seasonal adjustment
6992:Poisson regressions
6912:Bayesian regression
6851:Regression analysis
6831:Partial correlation
6803:Regression analysis
6402:Prediction interval
6397:Likelihood interval
6387:Confidence interval
6379:Interval estimation
6340:Unbiased estimators
6158:Model specification
6038:Up-and-down designs
5726:Partial correlation
5682:Index of dispersion
5600:Interquartile range
5380:Stochastic analysis
5220:Quadratic variation
5215:Prokhorov's theorem
5150:FeynmanâKac formula
4620:Markov random field
4268:Birthâdeath process
2839:The notation ARMAX(
2329:) is documented in
2241:for an estimate of
2233:for an estimate of
1982:{\displaystyle i=0}
1633:or more concisely,
364:, the roots of its
7640:Spatial statistics
7520:Medical statistics
7420:First hitting time
7374:Whittle likelihood
7025:Degrees of freedom
7020:Multivariate ANOVA
6953:Heteroscedasticity
6765:Bayesian estimator
6730:Bayesian inference
6579:KolmogorovâSmirnov
6464:Randomization test
6434:Testing hypotheses
6407:Tolerance interval
6318:Maximum likelihood
6213:Exponential family
6146:Density estimation
6106:Statistical theory
6066:Natural experiment
6012:Scientific control
5929:Survey methodology
5615:Standard deviation
5350:Probability theory
5230:Skorokhod integral
5200:Malliavin calculus
4783:Korn-Kreer-Lenssen
4667:Time series models
4630:PitmanâYor process
3495:
3405:
3375:
3171:
3138:
3089:
2902:. It is given by:
2892:
2805:(ARCH) models and
2772:
2755:The dependence of
2724:
2704:
2680:
2653:
2260:(AIC) for finding
2179:
2048:
2015:
1979:
1950:
1773:
1691:
1620:
1448:
1362:
1339:
1197:
1111:
1088:
913:
752:The notation ARMA(
734:
701:
674:
647:
627:
572:
443:
401:
335:
304:
255:
144:BoxâJenkins method
121:linear combination
105:
7742:
7741:
7680:
7679:
7676:
7675:
7615:National accounts
7585:Actuarial science
7577:Social statistics
7470:
7469:
7466:
7465:
7462:
7461:
7397:Survival function
7382:
7381:
7244:Granger causality
7085:Contingency table
7060:Survival analysis
7037:
7036:
7033:
7032:
6889:Linear regression
6784:
6783:
6780:
6779:
6755:Credible interval
6724:
6723:
6507:
6506:
6323:Method of moments
6192:Parametric family
6153:Statistical model
6083:
6082:
6079:
6078:
5997:Random assignment
5919:Statistical power
5853:
5852:
5849:
5848:
5698:Contingency table
5668:
5667:
5535:Generalized/power
5416:
5415:
5370:Signal processing
5089:Doob's upcrossing
5084:Doob's martingale
5048:EngelbertâSchmidt
4991:Donsker's theorem
4925:Feller-continuous
4793:RendlemanâBartter
4583:Dirichlet process
4500:Branching process
4469:Telegraph process
4362:Geometric process
4342:Empirical process
4332:Diffusion process
4188:Branching process
4183:Bernoulli process
4049:, R documentation
3740:978-1-118-67492-5
3606:
3605:
3598:
2641:
2578:
1744:
16:(Redirected from
7762:
7730:
7729:
7718:
7717:
7707:
7706:
7692:
7691:
7595:Crime statistics
7489:
7488:
7476:
7475:
7393:
7392:
7359:Fourier analysis
7346:Frequency domain
7326:
7273:
7239:Structural break
7199:
7198:
7148:Cluster analysis
7095:Log-linear model
7068:
7067:
7043:
7042:
6984:
6958:Homoscedasticity
6814:
6813:
6790:
6789:
6709:
6701:
6693:
6692:(KruskalâWallis)
6677:
6662:
6617:Cross validation
6602:
6584:AndersonâDarling
6531:
6518:
6517:
6489:Likelihood-ratio
6481:Parametric tests
6459:Permutation test
6442:1- & 2-tails
6333:Minimum distance
6305:Point estimation
6301:
6300:
6252:Optimal decision
6203:
6102:
6101:
6089:
6088:
6071:Quasi-experiment
6021:Adaptive designs
5872:
5871:
5859:
5858:
5736:Rank correlation
5498:
5497:
5489:
5488:
5476:
5475:
5443:
5436:
5429:
5420:
5419:
5390:Machine learning
5277:Usual hypotheses
5160:Girsanov theorem
5145:Dynkin's formula
4910:Continuous paths
4818:Actuarial models
4758:GarmanâKohlhagen
4728:BlackâKarasinski
4723:BlackâDermanâToy
4710:Financial models
4576:Fields and other
4505:Gaussian process
4454:Sigma-martingale
4258:Additive process
4160:
4153:
4146:
4137:
4136:
4122:
4121:
4104:
4085:
4073:
4050:
4044:
4038:
4037:
4009:
4003:
4002:
3974:
3968:
3956:
3950:
3949:
3931:
3925:
3924:
3922:
3913:
3907:
3906:
3888:
3882:
3881:
3866:
3860:
3857:
3840:Republished as:
3837:
3820:
3812:
3806:
3805:
3794:
3788:
3787:
3759:
3753:
3752:
3724:
3718:
3717:
3689:
3683:
3682:
3654:
3648:
3647:
3619:
3601:
3594:
3590:
3587:
3581:
3576:this article by
3567:inline citations
3554:
3553:
3546:
3504:
3502:
3501:
3496:
3490:
3489:
3474:
3473:
3463:
3458:
3434:
3433:
3414:
3412:
3411:
3406:
3404:
3403:
3384:
3382:
3381:
3376:
3370:
3369:
3354:
3353:
3343:
3338:
3317:
3316:
3298:
3297:
3279:
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3268:
3263:
3245:
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3231:
3219:
3218:
3180:
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3172:
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3169:
3147:
3145:
3144:
3139:
3137:
3136:
3118:
3117:
3098:
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3090:
3084:
3083:
3068:
3067:
3057:
3052:
3034:
3033:
3018:
3017:
3007:
3002:
2984:
2983:
2968:
2967:
2957:
2952:
2934:
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2921:
2920:
2901:
2899:
2898:
2893:
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2890:
2781:
2779:
2778:
2773:
2771:
2770:
2733:
2731:
2730:
2725:
2713:
2711:
2710:
2705:
2689:
2687:
2686:
2681:
2679:
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2659:
2654:
2652:
2651:
2646:
2642:
2640:
2636:
2635:
2613:
2609:
2608:
2586:
2579:
2577:
2569:
2568:
2559:
2534:spectral density
2209:Choosing p and q
2188:
2186:
2185:
2180:
2174:
2173:
2163:
2162:
2153:
2152:
2142:
2137:
2119:
2118:
2108:
2107:
2098:
2097:
2087:
2082:
2057:
2055:
2054:
2049:
2041:
2040:
2024:
2022:
2021:
2016:
2005:
2004:
1988:
1986:
1985:
1980:
1959:
1957:
1956:
1951:
1945:
1944:
1935:
1931:
1930:
1929:
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1371:
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1363:
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1273:
1268:
1233:
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1206:
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1203:
1198:
1192:
1191:
1182:
1181:
1171:
1166:
1120:
1118:
1117:
1112:
1097:
1095:
1094:
1089:
1086:
1085:
1061:
1060:
1051:
1047:
1046:
1045:
1036:
1035:
1025:
1020:
991:
990:
940:George E. P. Box
936:Fourier analysis
922:
920:
919:
914:
908:
907:
892:
891:
881:
876:
858:
857:
842:
841:
831:
826:
808:
807:
795:
794:
743:
741:
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735:
733:
732:
710:
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581:
579:
578:
573:
570:
569:
554:
553:
543:
538:
520:
519:
501:
500:
474:The notation MA(
452:
450:
449:
444:
433:
432:
410:
408:
407:
402:
394:
389:
388:
379:
344:
342:
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313:
311:
310:
305:
303:
302:
284:
283:
264:
262:
261:
256:
254:
253:
241:
240:
225:
224:
214:
209:
191:
190:
160:The notation AR(
114:
112:
111:
106:
104:
103:
79:George E. P. Box
21:
7770:
7769:
7765:
7764:
7763:
7761:
7760:
7759:
7755:Autocorrelation
7745:
7744:
7743:
7738:
7701:
7672:
7634:
7571:
7557:quality control
7524:
7506:Clinical trials
7483:
7458:
7442:
7430:Hazard function
7424:
7378:
7340:
7324:
7287:
7283:BreuschâGodfrey
7271:
7248:
7188:
7163:Factor analysis
7109:
7090:Graphical model
7062:
7029:
6996:
6982:
6962:
6916:
6883:
6845:
6808:
6807:
6776:
6720:
6707:
6699:
6691:
6675:
6660:
6639:Rank statistics
6633:
6612:Model selection
6600:
6558:Goodness of fit
6552:
6529:
6503:
6475:
6428:
6373:
6362:Median unbiased
6290:
6201:
6134:Order statistic
6096:
6075:
6042:
6016:
5968:
5923:
5866:
5864:Data collection
5845:
5757:
5712:
5686:
5664:
5624:
5576:
5493:Continuous data
5483:
5470:
5452:
5447:
5417:
5412:
5394:
5355:Queueing theory
5298:
5240:Skorokhod space
5103:
5094:KunitaâWatanabe
5065:
5031:Sanov's theorem
5001:Ergodic theorem
4974:
4970:Time-reversible
4888:
4851:Queueing models
4845:
4841:SparreâAnderson
4831:CramĂ©râLundberg
4812:
4798:SABR volatility
4704:
4661:
4613:Boolean network
4571:
4557:Renewal process
4488:
4437:Non-homogeneous
4427:Poisson process
4317:Contact process
4280:Brownian motion
4250:Continuous time
4244:
4238:Maximal entropy
4169:
4164:
4119:10.1.1.721.1754
4101:
4082:
4062:
4060:Further reading
4056:
4054:
4053:
4045:
4041:
4026:
4010:
4006:
3991:
3975:
3971:
3966:Wayback Machine
3957:
3953:
3946:
3932:
3928:
3920:
3914:
3910:
3903:
3889:
3885:
3867:
3863:
3854:
3834:
3813:
3809:
3795:
3791:
3776:
3760:
3756:
3741:
3725:
3721:
3706:
3690:
3686:
3671:
3655:
3651:
3636:
3620:
3616:
3611:
3602:
3591:
3585:
3582:
3572:Please help to
3571:
3555:
3551:
3511:
3479:
3475:
3469:
3465:
3459:
3448:
3429:
3425:
3423:
3420:
3419:
3399:
3395:
3393:
3390:
3389:
3359:
3355:
3349:
3345:
3339:
3328:
3306:
3302:
3287:
3283:
3274:
3270:
3264:
3253:
3240:
3236:
3227:
3223:
3214:
3210:
3208:
3205:
3204:
3165:
3161:
3159:
3156:
3155:
3132:
3128:
3113:
3109:
3107:
3104:
3103:
3073:
3069:
3063:
3059:
3053:
3042:
3023:
3019:
3013:
3009:
3003:
2992:
2973:
2969:
2963:
2959:
2953:
2942:
2929:
2925:
2916:
2912:
2910:
2907:
2906:
2886:
2882:
2880:
2877:
2876:
2837:
2798:(NARMA) model.
2785:
2766:
2762:
2760:
2757:
2756:
2753:
2751:Generalizations
2740:
2719:
2716:
2715:
2699:
2696:
2695:
2674:
2670:
2668:
2665:
2664:
2647:
2625:
2621:
2614:
2598:
2594:
2587:
2585:
2581:
2580:
2570:
2564:
2560:
2558:
2541:
2538:
2537:
2530:
2314:
2278:
2211:
2206:
2194:
2169:
2165:
2158:
2154:
2148:
2144:
2138:
2127:
2114:
2110:
2103:
2099:
2093:
2089:
2083:
2072:
2063:
2060:
2059:
2036:
2032:
2030:
2027:
2026:
2000:
1996:
1994:
1991:
1990:
1968:
1965:
1964:
1940:
1936:
1925:
1921:
1915:
1911:
1905:
1894:
1883:
1879:
1870:
1866:
1855:
1851:
1845:
1841:
1835:
1824:
1813:
1809:
1807:
1804:
1803:
1789:
1763:
1759:
1750:
1746:
1730:
1716:
1714:
1712:
1709:
1708:
1684:
1680:
1659:
1655:
1641:
1638:
1637:
1610:
1606:
1595:
1591:
1585:
1581:
1575:
1564:
1553:
1549:
1540:
1536:
1525:
1521:
1515:
1511:
1505:
1494:
1483:
1479:
1477:
1474:
1473:
1438:
1434:
1428:
1424:
1418:
1407:
1380:
1377:
1376:
1357:
1354:
1353:
1329:
1325:
1304:
1300:
1289:
1285:
1279:
1275:
1269:
1258:
1247:
1243:
1228:
1224:
1222:
1219:
1218:
1187:
1183:
1177:
1173:
1167:
1156:
1129:
1126:
1125:
1106:
1103:
1102:
1081:
1077:
1056:
1052:
1041:
1037:
1031:
1027:
1021:
1010:
999:
995:
986:
982:
980:
977:
976:
959:
897:
893:
887:
883:
877:
866:
847:
843:
837:
833:
827:
816:
803:
799:
790:
786:
784:
781:
780:
750:
722:
718:
716:
713:
712:
695:
691:
689:
686:
685:
668:
664:
662:
659:
658:
642:
639:
638:
621:
617:
596:
592:
590:
587:
586:
559:
555:
549:
545:
539:
528:
515:
511:
496:
492:
490:
487:
486:
472:
466:
428:
424:
416:
413:
412:
390:
384:
380:
375:
373:
370:
369:
329:
325:
323:
320:
319:
298:
294:
279:
275:
273:
270:
269:
249:
245:
230:
226:
220:
216:
210:
199:
186:
182:
180:
177:
176:
158:
152:
99:
95:
93:
90:
89:
35:
28:
23:
22:
15:
12:
11:
5:
7768:
7758:
7757:
7740:
7739:
7737:
7736:
7724:
7712:
7698:
7685:
7682:
7681:
7678:
7677:
7674:
7673:
7671:
7670:
7665:
7660:
7655:
7650:
7644:
7642:
7636:
7635:
7633:
7632:
7627:
7622:
7617:
7612:
7607:
7602:
7597:
7592:
7587:
7581:
7579:
7573:
7572:
7570:
7569:
7564:
7559:
7550:
7545:
7540:
7534:
7532:
7526:
7525:
7523:
7522:
7517:
7512:
7503:
7501:Bioinformatics
7497:
7495:
7485:
7484:
7472:
7471:
7468:
7467:
7464:
7463:
7460:
7459:
7457:
7456:
7450:
7448:
7444:
7443:
7441:
7440:
7434:
7432:
7426:
7425:
7423:
7422:
7417:
7412:
7407:
7401:
7399:
7390:
7384:
7383:
7380:
7379:
7377:
7376:
7371:
7366:
7361:
7356:
7350:
7348:
7342:
7341:
7339:
7338:
7333:
7328:
7320:
7315:
7310:
7309:
7308:
7306:partial (PACF)
7297:
7295:
7289:
7288:
7286:
7285:
7280:
7275:
7267:
7262:
7256:
7254:
7253:Specific tests
7250:
7249:
7247:
7246:
7241:
7236:
7231:
7226:
7221:
7216:
7211:
7205:
7203:
7196:
7190:
7189:
7187:
7186:
7185:
7184:
7183:
7182:
7167:
7166:
7165:
7155:
7153:Classification
7150:
7145:
7140:
7135:
7130:
7125:
7119:
7117:
7111:
7110:
7108:
7107:
7102:
7100:McNemar's test
7097:
7092:
7087:
7082:
7076:
7074:
7064:
7063:
7039:
7038:
7035:
7034:
7031:
7030:
7028:
7027:
7022:
7017:
7012:
7006:
7004:
6998:
6997:
6995:
6994:
6978:
6972:
6970:
6964:
6963:
6961:
6960:
6955:
6950:
6945:
6940:
6938:Semiparametric
6935:
6930:
6924:
6922:
6918:
6917:
6915:
6914:
6909:
6904:
6899:
6893:
6891:
6885:
6884:
6882:
6881:
6876:
6871:
6866:
6861:
6855:
6853:
6847:
6846:
6844:
6843:
6838:
6833:
6828:
6822:
6820:
6810:
6809:
6806:
6805:
6800:
6794:
6786:
6785:
6782:
6781:
6778:
6777:
6775:
6774:
6773:
6772:
6762:
6757:
6752:
6751:
6750:
6745:
6734:
6732:
6726:
6725:
6722:
6721:
6719:
6718:
6713:
6712:
6711:
6703:
6695:
6679:
6676:(MannâWhitney)
6671:
6670:
6669:
6656:
6655:
6654:
6643:
6641:
6635:
6634:
6632:
6631:
6630:
6629:
6624:
6619:
6609:
6604:
6601:(ShapiroâWilk)
6596:
6591:
6586:
6581:
6576:
6568:
6562:
6560:
6554:
6553:
6551:
6550:
6542:
6533:
6521:
6515:
6513:Specific tests
6509:
6508:
6505:
6504:
6502:
6501:
6496:
6491:
6485:
6483:
6477:
6476:
6474:
6473:
6468:
6467:
6466:
6456:
6455:
6454:
6444:
6438:
6436:
6430:
6429:
6427:
6426:
6425:
6424:
6419:
6409:
6404:
6399:
6394:
6389:
6383:
6381:
6375:
6374:
6372:
6371:
6366:
6365:
6364:
6359:
6358:
6357:
6352:
6337:
6336:
6335:
6330:
6325:
6320:
6309:
6307:
6298:
6292:
6291:
6289:
6288:
6283:
6278:
6277:
6276:
6266:
6261:
6260:
6259:
6249:
6248:
6247:
6242:
6237:
6227:
6222:
6217:
6216:
6215:
6210:
6205:
6189:
6188:
6187:
6182:
6177:
6167:
6166:
6165:
6160:
6150:
6149:
6148:
6138:
6137:
6136:
6126:
6121:
6116:
6110:
6108:
6098:
6097:
6085:
6084:
6081:
6080:
6077:
6076:
6074:
6073:
6068:
6063:
6058:
6052:
6050:
6044:
6043:
6041:
6040:
6035:
6030:
6024:
6022:
6018:
6017:
6015:
6014:
6009:
6004:
5999:
5994:
5989:
5984:
5978:
5976:
5970:
5969:
5967:
5966:
5964:Standard error
5961:
5956:
5951:
5950:
5949:
5944:
5933:
5931:
5925:
5924:
5922:
5921:
5916:
5911:
5906:
5901:
5896:
5894:Optimal design
5891:
5886:
5880:
5878:
5868:
5867:
5855:
5854:
5851:
5850:
5847:
5846:
5844:
5843:
5838:
5833:
5828:
5823:
5818:
5813:
5808:
5803:
5798:
5793:
5788:
5783:
5778:
5773:
5767:
5765:
5759:
5758:
5756:
5755:
5750:
5749:
5748:
5743:
5733:
5728:
5722:
5720:
5714:
5713:
5711:
5710:
5705:
5700:
5694:
5692:
5691:Summary tables
5688:
5687:
5685:
5684:
5678:
5676:
5670:
5669:
5666:
5665:
5663:
5662:
5661:
5660:
5655:
5650:
5640:
5634:
5632:
5626:
5625:
5623:
5622:
5617:
5612:
5607:
5602:
5597:
5592:
5586:
5584:
5578:
5577:
5575:
5574:
5569:
5564:
5563:
5562:
5557:
5552:
5547:
5542:
5537:
5532:
5527:
5525:Contraharmonic
5522:
5517:
5506:
5504:
5495:
5485:
5484:
5472:
5471:
5469:
5468:
5463:
5457:
5454:
5453:
5446:
5445:
5438:
5431:
5423:
5414:
5413:
5411:
5410:
5405:
5403:List of topics
5399:
5396:
5395:
5393:
5392:
5387:
5382:
5377:
5372:
5367:
5362:
5360:Renewal theory
5357:
5352:
5347:
5342:
5337:
5332:
5327:
5325:Ergodic theory
5322:
5317:
5315:Control theory
5312:
5306:
5304:
5300:
5299:
5297:
5296:
5295:
5294:
5289:
5279:
5274:
5269:
5264:
5259:
5258:
5257:
5247:
5245:Snell envelope
5242:
5237:
5232:
5227:
5222:
5217:
5212:
5207:
5202:
5197:
5192:
5187:
5182:
5177:
5172:
5167:
5162:
5157:
5152:
5147:
5142:
5137:
5132:
5127:
5122:
5117:
5111:
5109:
5105:
5104:
5102:
5101:
5096:
5091:
5086:
5081:
5075:
5073:
5067:
5066:
5064:
5063:
5044:BorelâCantelli
5033:
5028:
5023:
5018:
5013:
5008:
5003:
4998:
4993:
4988:
4982:
4980:
4979:Limit theorems
4976:
4975:
4973:
4972:
4967:
4962:
4957:
4952:
4947:
4942:
4937:
4932:
4927:
4922:
4917:
4912:
4907:
4902:
4896:
4894:
4890:
4889:
4887:
4886:
4881:
4876:
4871:
4866:
4861:
4855:
4853:
4847:
4846:
4844:
4843:
4838:
4833:
4828:
4822:
4820:
4814:
4813:
4811:
4810:
4805:
4800:
4795:
4790:
4785:
4780:
4775:
4770:
4765:
4760:
4755:
4750:
4745:
4740:
4735:
4730:
4725:
4720:
4714:
4712:
4706:
4705:
4703:
4702:
4697:
4692:
4687:
4682:
4677:
4671:
4669:
4663:
4662:
4660:
4659:
4654:
4649:
4648:
4647:
4642:
4632:
4627:
4622:
4617:
4616:
4615:
4610:
4600:
4598:Hopfield model
4595:
4590:
4585:
4579:
4577:
4573:
4572:
4570:
4569:
4564:
4559:
4554:
4549:
4544:
4543:
4542:
4537:
4532:
4527:
4517:
4515:Markov process
4512:
4507:
4502:
4496:
4494:
4490:
4489:
4487:
4486:
4484:Wiener sausage
4481:
4479:Wiener process
4476:
4471:
4466:
4461:
4459:Stable process
4456:
4451:
4449:Semimartingale
4446:
4441:
4440:
4439:
4434:
4424:
4419:
4414:
4409:
4404:
4399:
4394:
4392:Jump diffusion
4389:
4384:
4379:
4374:
4369:
4367:Hawkes process
4364:
4359:
4354:
4349:
4347:Feller process
4344:
4339:
4334:
4329:
4324:
4319:
4314:
4312:Cauchy process
4309:
4308:
4307:
4302:
4297:
4292:
4287:
4277:
4276:
4275:
4265:
4263:Bessel process
4260:
4254:
4252:
4246:
4245:
4243:
4242:
4241:
4240:
4235:
4230:
4225:
4215:
4210:
4205:
4200:
4195:
4190:
4185:
4179:
4177:
4171:
4170:
4163:
4162:
4155:
4148:
4140:
4134:
4133:
4124:
4105:
4099:
4086:
4080:
4061:
4058:
4052:
4051:
4039:
4024:
4004:
3989:
3969:
3951:
3944:
3926:
3908:
3901:
3883:
3861:
3859:
3858:
3852:
3832:
3807:
3789:
3774:
3754:
3739:
3719:
3704:
3684:
3669:
3649:
3634:
3613:
3612:
3610:
3607:
3604:
3603:
3558:
3556:
3549:
3544:
3543:
3538:
3533:
3528:
3523:
3518:
3510:
3507:
3506:
3505:
3493:
3488:
3485:
3482:
3478:
3472:
3468:
3462:
3457:
3454:
3451:
3447:
3443:
3440:
3437:
3432:
3428:
3402:
3398:
3386:
3385:
3373:
3368:
3365:
3362:
3358:
3352:
3348:
3342:
3337:
3334:
3331:
3327:
3323:
3320:
3315:
3312:
3309:
3305:
3301:
3296:
3293:
3290:
3286:
3282:
3277:
3273:
3267:
3262:
3259:
3256:
3252:
3248:
3243:
3239:
3235:
3230:
3226:
3222:
3217:
3213:
3168:
3164:
3135:
3131:
3127:
3124:
3121:
3116:
3112:
3100:
3099:
3087:
3082:
3079:
3076:
3072:
3066:
3062:
3056:
3051:
3048:
3045:
3041:
3037:
3032:
3029:
3026:
3022:
3016:
3012:
3006:
3001:
2998:
2995:
2991:
2987:
2982:
2979:
2976:
2972:
2966:
2962:
2956:
2951:
2948:
2945:
2941:
2937:
2932:
2928:
2924:
2919:
2915:
2889:
2885:
2836:
2833:
2783:
2769:
2765:
2752:
2749:
2745:mean-reversion
2739:
2736:
2723:
2703:
2677:
2673:
2650:
2645:
2639:
2634:
2631:
2628:
2624:
2620:
2617:
2612:
2607:
2604:
2601:
2597:
2593:
2590:
2584:
2576:
2573:
2567:
2563:
2557:
2554:
2551:
2548:
2545:
2529:
2526:
2525:
2524:
2514:
2503:
2485:
2475:
2465:
2459:
2453:
2438:
2426:
2394:
2388:
2333:. The package
2313:
2310:
2277:
2274:
2210:
2207:
2205:
2204:Fitting models
2202:
2193:
2190:
2178:
2172:
2168:
2161:
2157:
2151:
2147:
2141:
2136:
2133:
2130:
2126:
2122:
2117:
2113:
2106:
2102:
2096:
2092:
2086:
2081:
2078:
2075:
2071:
2067:
2047:
2044:
2039:
2035:
2014:
2011:
2008:
2003:
1999:
1978:
1975:
1972:
1961:
1960:
1949:
1943:
1939:
1934:
1928:
1924:
1918:
1914:
1908:
1903:
1900:
1897:
1893:
1889:
1886:
1882:
1878:
1873:
1869:
1864:
1858:
1854:
1848:
1844:
1838:
1833:
1830:
1827:
1823:
1819:
1816:
1812:
1788:
1785:
1784:
1783:
1772:
1766:
1762:
1758:
1753:
1749:
1742:
1739:
1736:
1733:
1728:
1725:
1722:
1719:
1702:
1701:
1687:
1683:
1679:
1676:
1673:
1670:
1667:
1662:
1658:
1654:
1651:
1648:
1645:
1631:
1630:
1619:
1613:
1609:
1604:
1598:
1594:
1588:
1584:
1578:
1573:
1570:
1567:
1563:
1559:
1556:
1552:
1548:
1543:
1539:
1534:
1528:
1524:
1518:
1514:
1508:
1503:
1500:
1497:
1493:
1489:
1486:
1482:
1459:
1458:
1446:
1441:
1437:
1431:
1427:
1421:
1416:
1413:
1410:
1406:
1402:
1399:
1396:
1393:
1390:
1387:
1384:
1361:
1350:
1349:
1337:
1332:
1328:
1324:
1321:
1318:
1315:
1312:
1307:
1303:
1298:
1292:
1288:
1282:
1278:
1272:
1267:
1264:
1261:
1257:
1253:
1250:
1246:
1242:
1239:
1236:
1231:
1227:
1208:
1207:
1195:
1190:
1186:
1180:
1176:
1170:
1165:
1162:
1159:
1155:
1151:
1148:
1145:
1142:
1139:
1136:
1133:
1110:
1099:
1098:
1084:
1080:
1076:
1073:
1070:
1067:
1064:
1059:
1055:
1050:
1044:
1040:
1034:
1030:
1024:
1019:
1016:
1013:
1009:
1005:
1002:
998:
994:
989:
985:
958:
955:
932:Laurent series
924:
923:
911:
906:
903:
900:
896:
890:
886:
880:
875:
872:
869:
865:
861:
856:
853:
850:
846:
840:
836:
830:
825:
822:
819:
815:
811:
806:
802:
798:
793:
789:
749:
746:
731:
728:
725:
721:
698:
694:
671:
667:
646:
624:
620:
616:
613:
610:
607:
604:
599:
595:
583:
582:
568:
565:
562:
558:
552:
548:
542:
537:
534:
531:
527:
523:
518:
514:
510:
507:
504:
499:
495:
468:Main article:
465:
462:
442:
439:
436:
431:
427:
423:
420:
400:
397:
393:
387:
383:
378:
332:
328:
301:
297:
293:
290:
287:
282:
278:
266:
265:
252:
248:
244:
239:
236:
233:
229:
223:
219:
213:
208:
205:
202:
198:
194:
189:
185:
154:Main article:
151:
148:
131:) model where
102:
98:
83:Gwilym Jenkins
67:moving average
63:autoregression
26:
9:
6:
4:
3:
2:
7767:
7756:
7753:
7752:
7750:
7735:
7734:
7725:
7723:
7722:
7713:
7711:
7710:
7705:
7699:
7697:
7696:
7687:
7686:
7683:
7669:
7666:
7664:
7663:Geostatistics
7661:
7659:
7656:
7654:
7651:
7649:
7646:
7645:
7643:
7641:
7637:
7631:
7630:Psychometrics
7628:
7626:
7623:
7621:
7618:
7616:
7613:
7611:
7608:
7606:
7603:
7601:
7598:
7596:
7593:
7591:
7588:
7586:
7583:
7582:
7580:
7578:
7574:
7568:
7565:
7563:
7560:
7558:
7554:
7551:
7549:
7546:
7544:
7541:
7539:
7536:
7535:
7533:
7531:
7527:
7521:
7518:
7516:
7513:
7511:
7507:
7504:
7502:
7499:
7498:
7496:
7494:
7493:Biostatistics
7490:
7486:
7482:
7477:
7473:
7455:
7454:Log-rank test
7452:
7451:
7449:
7445:
7439:
7436:
7435:
7433:
7431:
7427:
7421:
7418:
7416:
7413:
7411:
7408:
7406:
7403:
7402:
7400:
7398:
7394:
7391:
7389:
7385:
7375:
7372:
7370:
7367:
7365:
7362:
7360:
7357:
7355:
7352:
7351:
7349:
7347:
7343:
7337:
7334:
7332:
7329:
7327:
7325:(BoxâJenkins)
7321:
7319:
7316:
7314:
7311:
7307:
7304:
7303:
7302:
7299:
7298:
7296:
7294:
7290:
7284:
7281:
7279:
7278:DurbinâWatson
7276:
7274:
7268:
7266:
7263:
7261:
7260:DickeyâFuller
7258:
7257:
7255:
7251:
7245:
7242:
7240:
7237:
7235:
7234:Cointegration
7232:
7230:
7227:
7225:
7222:
7220:
7217:
7215:
7212:
7210:
7209:Decomposition
7207:
7206:
7204:
7200:
7197:
7195:
7191:
7181:
7178:
7177:
7176:
7173:
7172:
7171:
7168:
7164:
7161:
7160:
7159:
7156:
7154:
7151:
7149:
7146:
7144:
7141:
7139:
7136:
7134:
7131:
7129:
7126:
7124:
7121:
7120:
7118:
7116:
7112:
7106:
7103:
7101:
7098:
7096:
7093:
7091:
7088:
7086:
7083:
7081:
7080:Cohen's kappa
7078:
7077:
7075:
7073:
7069:
7065:
7061:
7057:
7053:
7049:
7044:
7040:
7026:
7023:
7021:
7018:
7016:
7013:
7011:
7008:
7007:
7005:
7003:
6999:
6993:
6989:
6985:
6979:
6977:
6974:
6973:
6971:
6969:
6965:
6959:
6956:
6954:
6951:
6949:
6946:
6944:
6941:
6939:
6936:
6934:
6933:Nonparametric
6931:
6929:
6926:
6925:
6923:
6919:
6913:
6910:
6908:
6905:
6903:
6900:
6898:
6895:
6894:
6892:
6890:
6886:
6880:
6877:
6875:
6872:
6870:
6867:
6865:
6862:
6860:
6857:
6856:
6854:
6852:
6848:
6842:
6839:
6837:
6834:
6832:
6829:
6827:
6824:
6823:
6821:
6819:
6815:
6811:
6804:
6801:
6799:
6796:
6795:
6791:
6787:
6771:
6768:
6767:
6766:
6763:
6761:
6758:
6756:
6753:
6749:
6746:
6744:
6741:
6740:
6739:
6736:
6735:
6733:
6731:
6727:
6717:
6714:
6710:
6704:
6702:
6696:
6694:
6688:
6687:
6686:
6683:
6682:Nonparametric
6680:
6678:
6672:
6668:
6665:
6664:
6663:
6657:
6653:
6652:Sample median
6650:
6649:
6648:
6645:
6644:
6642:
6640:
6636:
6628:
6625:
6623:
6620:
6618:
6615:
6614:
6613:
6610:
6608:
6605:
6603:
6597:
6595:
6592:
6590:
6587:
6585:
6582:
6580:
6577:
6575:
6573:
6569:
6567:
6564:
6563:
6561:
6559:
6555:
6549:
6547:
6543:
6541:
6539:
6534:
6532:
6527:
6523:
6522:
6519:
6516:
6514:
6510:
6500:
6497:
6495:
6492:
6490:
6487:
6486:
6484:
6482:
6478:
6472:
6469:
6465:
6462:
6461:
6460:
6457:
6453:
6450:
6449:
6448:
6445:
6443:
6440:
6439:
6437:
6435:
6431:
6423:
6420:
6418:
6415:
6414:
6413:
6410:
6408:
6405:
6403:
6400:
6398:
6395:
6393:
6390:
6388:
6385:
6384:
6382:
6380:
6376:
6370:
6367:
6363:
6360:
6356:
6353:
6351:
6348:
6347:
6346:
6343:
6342:
6341:
6338:
6334:
6331:
6329:
6326:
6324:
6321:
6319:
6316:
6315:
6314:
6311:
6310:
6308:
6306:
6302:
6299:
6297:
6293:
6287:
6284:
6282:
6279:
6275:
6272:
6271:
6270:
6267:
6265:
6262:
6258:
6257:loss function
6255:
6254:
6253:
6250:
6246:
6243:
6241:
6238:
6236:
6233:
6232:
6231:
6228:
6226:
6223:
6221:
6218:
6214:
6211:
6209:
6206:
6204:
6198:
6195:
6194:
6193:
6190:
6186:
6183:
6181:
6178:
6176:
6173:
6172:
6171:
6168:
6164:
6161:
6159:
6156:
6155:
6154:
6151:
6147:
6144:
6143:
6142:
6139:
6135:
6132:
6131:
6130:
6127:
6125:
6122:
6120:
6117:
6115:
6112:
6111:
6109:
6107:
6103:
6099:
6095:
6090:
6086:
6072:
6069:
6067:
6064:
6062:
6059:
6057:
6054:
6053:
6051:
6049:
6045:
6039:
6036:
6034:
6031:
6029:
6026:
6025:
6023:
6019:
6013:
6010:
6008:
6005:
6003:
6000:
5998:
5995:
5993:
5990:
5988:
5985:
5983:
5980:
5979:
5977:
5975:
5971:
5965:
5962:
5960:
5959:Questionnaire
5957:
5955:
5952:
5948:
5945:
5943:
5940:
5939:
5938:
5935:
5934:
5932:
5930:
5926:
5920:
5917:
5915:
5912:
5910:
5907:
5905:
5902:
5900:
5897:
5895:
5892:
5890:
5887:
5885:
5882:
5881:
5879:
5877:
5873:
5869:
5865:
5860:
5856:
5842:
5839:
5837:
5834:
5832:
5829:
5827:
5824:
5822:
5819:
5817:
5814:
5812:
5809:
5807:
5804:
5802:
5799:
5797:
5794:
5792:
5789:
5787:
5786:Control chart
5784:
5782:
5779:
5777:
5774:
5772:
5769:
5768:
5766:
5764:
5760:
5754:
5751:
5747:
5744:
5742:
5739:
5738:
5737:
5734:
5732:
5729:
5727:
5724:
5723:
5721:
5719:
5715:
5709:
5706:
5704:
5701:
5699:
5696:
5695:
5693:
5689:
5683:
5680:
5679:
5677:
5675:
5671:
5659:
5656:
5654:
5651:
5649:
5646:
5645:
5644:
5641:
5639:
5636:
5635:
5633:
5631:
5627:
5621:
5618:
5616:
5613:
5611:
5608:
5606:
5603:
5601:
5598:
5596:
5593:
5591:
5588:
5587:
5585:
5583:
5579:
5573:
5570:
5568:
5565:
5561:
5558:
5556:
5553:
5551:
5548:
5546:
5543:
5541:
5538:
5536:
5533:
5531:
5528:
5526:
5523:
5521:
5518:
5516:
5513:
5512:
5511:
5508:
5507:
5505:
5503:
5499:
5496:
5494:
5490:
5486:
5482:
5477:
5473:
5467:
5464:
5462:
5459:
5458:
5455:
5451:
5444:
5439:
5437:
5432:
5430:
5425:
5424:
5421:
5409:
5406:
5404:
5401:
5400:
5397:
5391:
5388:
5386:
5383:
5381:
5378:
5376:
5373:
5371:
5368:
5366:
5363:
5361:
5358:
5356:
5353:
5351:
5348:
5346:
5343:
5341:
5338:
5336:
5333:
5331:
5328:
5326:
5323:
5321:
5318:
5316:
5313:
5311:
5308:
5307:
5305:
5301:
5293:
5290:
5288:
5285:
5284:
5283:
5280:
5278:
5275:
5273:
5270:
5268:
5265:
5263:
5262:Stopping time
5260:
5256:
5253:
5252:
5251:
5248:
5246:
5243:
5241:
5238:
5236:
5233:
5231:
5228:
5226:
5223:
5221:
5218:
5216:
5213:
5211:
5208:
5206:
5203:
5201:
5198:
5196:
5193:
5191:
5188:
5186:
5183:
5181:
5178:
5176:
5173:
5171:
5168:
5166:
5163:
5161:
5158:
5156:
5153:
5151:
5148:
5146:
5143:
5141:
5138:
5136:
5133:
5131:
5128:
5126:
5123:
5121:
5118:
5116:
5113:
5112:
5110:
5106:
5100:
5097:
5095:
5092:
5090:
5087:
5085:
5082:
5080:
5077:
5076:
5074:
5072:
5068:
5061:
5057:
5053:
5052:HewittâSavage
5049:
5045:
5041:
5037:
5036:Zeroâone laws
5034:
5032:
5029:
5027:
5024:
5022:
5019:
5017:
5014:
5012:
5009:
5007:
5004:
5002:
4999:
4997:
4994:
4992:
4989:
4987:
4984:
4983:
4981:
4977:
4971:
4968:
4966:
4963:
4961:
4958:
4956:
4953:
4951:
4948:
4946:
4943:
4941:
4938:
4936:
4933:
4931:
4928:
4926:
4923:
4921:
4918:
4916:
4913:
4911:
4908:
4906:
4903:
4901:
4898:
4897:
4895:
4891:
4885:
4882:
4880:
4877:
4875:
4872:
4870:
4867:
4865:
4862:
4860:
4857:
4856:
4854:
4852:
4848:
4842:
4839:
4837:
4834:
4832:
4829:
4827:
4824:
4823:
4821:
4819:
4815:
4809:
4806:
4804:
4801:
4799:
4796:
4794:
4791:
4789:
4786:
4784:
4781:
4779:
4776:
4774:
4771:
4769:
4766:
4764:
4761:
4759:
4756:
4754:
4751:
4749:
4746:
4744:
4741:
4739:
4736:
4734:
4733:BlackâScholes
4731:
4729:
4726:
4724:
4721:
4719:
4716:
4715:
4713:
4711:
4707:
4701:
4698:
4696:
4693:
4691:
4688:
4686:
4683:
4681:
4678:
4676:
4673:
4672:
4670:
4668:
4664:
4658:
4655:
4653:
4650:
4646:
4643:
4641:
4638:
4637:
4636:
4635:Point process
4633:
4631:
4628:
4626:
4623:
4621:
4618:
4614:
4611:
4609:
4606:
4605:
4604:
4601:
4599:
4596:
4594:
4593:Gibbs measure
4591:
4589:
4586:
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4382:ItĂŽ diffusion
4380:
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4357:Gamma process
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4228:Self-avoiding
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4213:Moran process
4211:
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4175:Discrete time
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4025:0-201-15911-2
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3992:
3990:0-387-98917-X
3986:
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3945:9781441903198
3941:
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3879:
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3874:Hannan, E. J.
3870:
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3855:
3853:0-8166-1148-3
3849:
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3833:0-8166-1147-5
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933:
929:
928:Peter Whittle
909:
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460:time series.
458:
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71:Peter Whittle
68:
64:
60:
56:
52:
48:
44:
40:
33:
19:
7731:
7719:
7700:
7693:
7605:Econometrics
7555: /
7538:Chemometrics
7515:Epidemiology
7508: /
7481:Applications
7323:ARIMA model
7270:Q-statistic
7219:Stationarity
7115:Multivariate
7058: /
7054: /
7052:Multivariate
7050: /
6990: /
6986: /
6760:Bayes factor
6659:Signed rank
6571:
6545:
6537:
6525:
6220:Completeness
6056:Cohort study
5954:Opinion poll
5889:Missing data
5876:Study design
5831:Scatter plot
5753:Scatter plot
5746:Spearman's Ï
5708:Grouped data
5320:Econometrics
5282:Wiener space
5170:ItĂŽ integral
5071:Inequalities
4960:Self-similar
4930:GaussâMarkov
4920:Exchangeable
4900:CĂ dlĂ g paths
4836:Risk process
4788:LIBOR market
4657:Random graph
4652:Random field
4464:Superprocess
4402:LĂ©vy process
4397:Jump process
4372:Hunt process
4208:Markov chain
4128:
4109:
4090:
4069:
4055:
4042:
4014:
4007:
3979:
3972:
3954:
3935:
3929:
3911:
3892:
3886:
3877:
3864:
3843:
3823:
3816:
3810:
3801:
3792:
3764:
3757:
3729:
3722:
3694:
3687:
3659:
3652:
3624:
3617:
3592:
3583:
3564:
3387:
3190:
3183:
3150:
3149:
3101:
2872:
2868:
2864:
2860:
2856:
2852:
2848:
2844:
2840:
2838:
2824:
2822:
2817:
2815:
2800:
2795:
2791:
2787:
2754:
2741:
2738:Applications
2531:
2491:
2482:octave-forge
2442:scikit-learn
2433:
2413:
2407:
2401:
2380:
2376:
2370:
2365:
2359:
2350:
2346:
2342:
2338:
2326:
2322:
2306:
2297:
2293:
2288:, fitted by
2285:
2281:
2279:
2265:
2261:
2255:
2250:
2246:
2242:
2234:
2226:
2222:
2221:in the ARMA(
2218:
2214:
2212:
2195:
1989:and setting
1962:
1790:
1703:
1632:
1466:
1462:
1460:
1351:
1211:
1209:
1100:
969:
965:
963:lag operator
960:
948:
925:
773:
769:
765:
761:
757:
753:
751:
584:
479:
475:
473:
455:
359:
267:
169:
165:
161:
159:
141:
136:
132:
128:
124:
87:
74:
54:
50:
46:
41:analysis of
36:
7733:WikiProject
7648:Cartography
7610:Jurimetrics
7562:Reliability
7293:Time domain
7272:(LjungâBox)
7194:Time-series
7072:Categorical
7056:Time-series
7048:Categorical
6983:(Bernoulli)
6818:Correlation
6798:Correlation
6594:JarqueâBera
6566:Chi-squared
6328:M-estimator
6281:Asymptotics
6225:Sufficiency
5992:Interaction
5904:Replication
5884:Effect size
5841:Violin plot
5821:Radar chart
5801:Forest plot
5791:Correlogram
5741:Kendall's Ï
5365:Ruin theory
5303:Disciplines
5175:ItĂŽ's lemma
4950:Predictable
4625:Percolation
4608:Potts model
4603:Ising model
4567:White noise
4525:Differences
4387:ItĂŽ process
4327:Cox process
4223:Loop-erased
4218:Random walk
3871:, p. 227):
3586:August 2010
3578:introducing
2391:Mathematica
2385:Time Series
2272:criterion.
944:BoxâJenkins
347:white noise
43:time series
39:statistical
7600:Demography
7318:ARMA model
7123:Regression
6700:(Friedman)
6661:(Wilcoxon)
6599:Normality
6589:Lilliefors
6536:Student's
6412:Resampling
6286:Robustness
6274:divergence
6264:Efficiency
6202:(monotone)
6197:Likelihood
6114:Population
5947:Stratified
5899:Population
5718:Dependence
5674:Count data
5605:Percentile
5582:Dispersion
5515:Arithmetic
5450:Statistics
5375:Statistics
5155:Filtration
5056:Kolmogorov
5040:Blumenthal
4965:Stationary
4905:Continuous
4893:Properties
4778:HullâWhite
4520:Martingale
4407:Local time
4295:Fractional
4273:pure birth
4100:052135532X
4081:0521343399
3902:0130607746
3609:References
3561:references
3151:parameters
2825:univariate
2794:(NAR), or
2478:GNU Octave
2377:auto.arima
2366:fracdiff()
2343:sarima.sim
776:) models,
748:ARMA model
585:where the
362:stationary
349:, usually
316:parameters
117:error term
6981:Logistic
6748:posterior
6674:Rank sum
6422:Jackknife
6417:Bootstrap
6235:Bootstrap
6170:Parameter
6119:Statistic
5914:Statistic
5826:Run chart
5811:Pie chart
5806:Histogram
5796:Fan chart
5771:Bar chart
5653:L-moments
5540:Geometric
5287:Classical
4300:Geometric
4290:Excursion
4114:CiteSeerX
3749:908107438
3484:−
3467:η
3446:∑
3364:−
3357:ε
3347:θ
3326:∑
3311:−
3300:−
3292:−
3272:φ
3251:∑
3238:ε
3221:−
3130:η
3123:…
3111:η
3078:−
3061:η
3040:∑
3028:−
3021:ε
3011:θ
2990:∑
2978:−
2961:φ
2940:∑
2927:ε
2867:) and MA(
2722:ϕ
2702:θ
2672:σ
2627:−
2616:ϕ
2600:−
2589:θ
2575:π
2562:σ
2375:includes
2364:contains
2167:ε
2146:θ
2125:∑
2091:ϕ
2070:∑
2066:−
2034:θ
2010:−
1998:ϕ
1938:ε
1913:θ
1892:∑
1843:ϕ
1822:∑
1818:−
1761:ε
1732:θ
1718:φ
1682:ε
1669:θ
1644:φ
1608:ε
1583:θ
1562:∑
1513:φ
1492:∑
1488:−
1426:θ
1405:∑
1383:θ
1360:θ
1327:ε
1314:θ
1302:ε
1277:θ
1256:∑
1238:μ
1235:−
1175:φ
1154:∑
1150:−
1132:φ
1109:φ
1066:φ
1029:φ
1008:∑
1004:−
984:ε
902:−
895:ε
885:θ
864:∑
852:−
835:φ
814:∑
801:ε
772:) and MA(
727:−
720:ε
693:ε
645:μ
619:θ
594:θ
564:−
557:ε
547:θ
526:∑
513:ε
506:μ
426:φ
422:−
396:≥
382:φ
353:(i.i.d.)
327:ε
296:φ
289:…
277:φ
247:ε
235:−
218:φ
197:∑
168:. The AR(
7749:Category
7695:Category
7388:Survival
7265:Johansen
6988:Binomial
6943:Isotonic
6530:(normal)
6175:location
5982:Blocking
5937:Sampling
5816:QâQ plot
5781:Box plot
5763:Graphics
5658:Skewness
5648:Kurtosis
5620:Variance
5550:Heronian
5545:Harmonic
5408:Category
5292:Abstract
4826:BĂŒhlmann
4432:Compound
4034:18166355
3999:42061096
3962:Archived
3800:(1970).
3784:42392178
3714:28888762
3679:42392178
3644:28888762
3509:See also
3148:are the
2692:variance
2528:Spectrum
2498:models.
2371:forecast
2360:fracdiff
7721:Commons
7668:Kriging
7553:Process
7510:studies
7369:Wavelet
7202:General
6369:Plug-in
6163:L space
5942:Cluster
5643:Moments
5461:Outline
4915:Ergodic
4803:VaĆĄĂÄek
4645:Poisson
4305:Meander
3574:improve
3517:(ARIMA)
2790:(NMA),
2690:is the
2506:SuanShu
2434:arma.jl
2373:package
2362:package
2347:tseries
1797:Jenkins
1210:The MA(
37:In the
7590:Census
7180:Normal
7128:Manova
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