1737:, it is not obvious how to get the method started. We could assume that the initial forecast is equal to the initial value of demand; however, this approach has a serious drawback. Exponential smoothing puts substantial weight on past observations, so the initial value of demand will have an unreasonably large effect on early forecasts. This problem can be overcome by allowing the process to evolve for a reasonable number of periods (10 or more) and using the average of the demand during those periods as the initial forecast. There are many other ways of setting this initial value, but it is important to note that the smaller the value of
9473:
9459:
5227:
6545:
9497:
9485:
4140:
4780:
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2622:
5612:
5222:{\displaystyle {\begin{aligned}s_{0}&=x_{0}\\s_{t}&=\alpha {\frac {x_{t}}{c_{t-L}}}+(1-\alpha )(s_{t-1}+b_{t-1})\\b_{t}&=\beta (s_{t}-s_{t-1})+(1-\beta )b_{t-1}\\c_{t}&=\gamma {\frac {x_{t}}{s_{t}}}+(1-\gamma )c_{t-L}\\F_{t+m}&=(s_{t}+mb_{t})c_{t-L+1+(m-1){\bmod {L}}},\end{aligned}}}
4323:
1280:
Unlike some other smoothing methods, such as the simple moving average, this technique does not require any minimum number of observations to be made before it begins to produce results. In practice, however, a "good average" will not be achieved until several samples have been averaged together; for
1799:
There are cases where the smoothing parameters may be chosen in a subjective manner â the forecaster specifies the value of the smoothing parameters based on previous experience. However, a more robust and objective way to obtain values of the unknown parameters included in any exponential smoothing
4351:
Triple exponential smoothing was first suggested by Holt's student, Peter
Winters, in 1960 after reading a signal processing book from the 1940s on exponential smoothing. Holt's novel idea was to repeat filtering an odd number of times greater than 1 and less than 5, which was popular with scholars
2844:
Exponential smoothing and moving average have similar defects of introducing a lag relative to the input data. While this can be corrected by shifting the result by half the window length for a symmetrical kernel, such as a moving average or gaussian, it is unclear how appropriate this would be for
6572:
includes Simple, Simple
Seasonal, Holt's Linear Trend, Brown's Linear Trend, Damped Trend, Winters' Additive, and Winters' Multiplicative in the Time-Series modeling procedure within its Statistics and Modeler statistical packages. The default Expert Modeler feature evaluates all seven exponential
2900:
in the data. In such situations, several methods were devised under the name "double exponential smoothing" or "second-order exponential smoothing," which is the recursive application of an exponential filter twice, thus being termed "double exponential smoothing". This nomenclature is similar to
42:
the past observations are weighted equally, exponential functions are used to assign exponentially decreasing weights over time. It is an easily learned and easily applied procedure for making some determination based on prior assumptions by the user, such as seasonality. Exponential smoothing is
2901:
quadruple exponential smoothing, which also references its recursion depth. The basic idea behind double exponential smoothing is to introduce a term to take into account the possibility of a series exhibiting some form of trend. This slope component is itself updated via exponential smoothing.
1309:
stages to reach 95% of the actual value. To accurately reconstruct the original signal without information loss, all stages of the exponential moving average must also be available, because older samples decay in weight exponentially. This is in contrast to a simple moving average, in which some
6540:{\displaystyle {\begin{aligned}s_{0}&=x_{0}\\s_{t}&=\alpha (x_{t}-c_{t-L})+(1-\alpha )(s_{t-1}+b_{t-1})\\b_{t}&=\beta (s_{t}-s_{t-1})+(1-\beta )b_{t-1}\\c_{t}&=\gamma (x_{t}-s_{t-1}-b_{t-1})+(1-\gamma )c_{t-L}\\F_{t+m}&=s_{t}+mb_{t}+c_{t-L+1+(m-1){\bmod {L}}},\end{aligned}}}
3502:
1310:
samples can be skipped without as much loss of information due to the constant weighting of samples within the average. If a known number of samples will be missed, one can adjust a weighted average for this as well, by giving equal weight to the new sample and all those to be skipped.
669:
in 1957. The formulation below, which is the one commonly used, is attributed to Brown and is known as "Brownâs simple exponential smoothing". All the methods of Holt, Winters and Brown may be seen as a simple application of recursive filtering, first found in the 1940s to convert
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4135:{\displaystyle {\begin{aligned}s'_{0}&=x_{0}\\s''_{0}&=x_{0}\\s'_{t}&=\alpha x_{t}+(1-\alpha )s'_{t-1}\\s''_{t}&=\alpha s'_{t}+(1-\alpha )s''_{t-1}\\F_{t+m}&=a_{t}+mb_{t},\end{aligned}}}
4182:
4177:
1536:
2617:{\displaystyle {\begin{aligned}s_{t}&=\alpha x_{t}+(1-\alpha )s_{t-1}\\&=\alpha x_{t}+\alpha (1-\alpha )x_{t-1}+(1-\alpha )^{2}s_{t-2}\\&=\alpha \left+(1-\alpha )^{t}x_{0}.\end{aligned}}}
1636:
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Unlike the regression case (where we have formulae to directly compute the regression coefficients which minimize the SSE) this involves a non-linear minimization problem, and we need to use an
222:
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is the number of past data points in consideration of moving average. They differ in that exponential smoothing takes into account all past data, whereas moving average only takes into account
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The method calculates a trend line for the data as well as seasonal indices that weight the values in the trend line based on where that time point falls in the cycle of length
3613:
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For every exponential smoothing method, we also need to choose the value for the smoothing parameters. For simple exponential smoothing, there is only one smoothing parameter (
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4337:
under study. There are different types of seasonality: 'multiplicative' and 'additive' in nature, much like addition and multiplication are basic operations in mathematics.
2040:
404:
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5607:{\displaystyle {\begin{aligned}b_{0}&={\frac {1}{L}}\left({\frac {x_{L+1}-x_{1}}{L}}+{\frac {x_{L+2}-x_{2}}{L}}+\cdots +{\frac {x_{L+L}-x_{L}}{L}}\right)\end{aligned}}}
2194:
The name 'exponential smoothing' is attributed to the use of the exponential window function during convolution. It is no longer attributed to Holt, Winters & Brown.
7176:
1917:
1307:
9535:
6559:: the HoltWinters function in the stats package and ets function in the forecast package (a more complete implementation, generally resulting in a better performance).
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Triple exponential smoothing applies exponential smoothing three times, which is commonly used when there are three high frequency signals to be removed from a
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2012:
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technique, rather than one based on theoretical foundations and has often been over-emphasized by practitioners. Suppose we have a sequence of observations
687:
3497:{\displaystyle {\begin{aligned}s_{t}&=\alpha x_{t}+(1-\alpha )(s_{t-1}+b_{t-1})\\b_{t}&=\beta (s_{t}-s_{t-1})+(1-\beta )b_{t-1}\\\end{aligned}}}
7142:
2869: + 1 plus the most recent forecast value, to be kept, whereas exponential smoothing only needs the most recent forecast value to be kept.
2724:
2034:(based on the previous data or prediction), respectively. Hence, we find the values of the unknown parameters and the initial values that minimize
9528:
8594:
9099:
4356:, while triple application required more than double the operations of singular convolution. The use of a triple application is considered a
3843:
A second method, referred to as either Brown's linear exponential smoothing (LES) or Brown's double exponential smoothing works as follows.
970:. Simple exponential smoothing is easily applied, and it produces a smoothed statistic as soon as two observations are available. The term
2845:
exponential smoothing. They (moving average with symmetrical kernels) also both have roughly the same distribution of forecast error when
9249:
8873:
7514:
1170:. Sometimes the statistician's judgment is used to choose an appropriate factor. Alternatively, a statistical technique may be used to
9521:
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6712:
8647:
1318:
4318:{\displaystyle {\begin{aligned}a_{t}&=2s'_{t}-s''_{t}\\b_{t}&={\frac {\alpha }{1-\alpha }}(s'_{t}-s''_{t}).\end{aligned}}}
9086:
1704:(the initial raw data or observation). Because exponential smoothing requires that, at each stage, we have the previous forecast
4352:
of previous eras. While recursive filtering had been used previously, it was applied twice and four times to coincide with the
1564:
is the sampling time interval of the discrete time implementation. If the sampling time is fast compared to the time constant (
1480:
1603:
6903:
7509:
7209:
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in nature. However, if we sell 10% more apartments in the summer months than we do in the winter months the seasonality is
2880:
is broadly used in this fashion, but a different terminology is used: exponential smoothing is equivalent to a first-order
8113:
7261:
6617:
1804:
7167:
6623:
340:{\displaystyle {\begin{aligned}s_{0}&=x_{0}\\s_{t}&=\alpha x_{t}+(1-\alpha )s_{t-1},\quad t>0\end{aligned}}}
1803:
The unknown parameters and the initial values for any exponential smoothing method can be estimated by minimizing the
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7181:
6887:
6695:
2657:
1810:
9501:
9074:
8948:
1427:
5843:{\displaystyle c_{i}={\frac {1}{N}}\sum _{j=1}^{N}{\frac {x_{L(j-1)+i}}{A_{j}}}\quad {\text{for }}i=1,2,\ldots ,L}
1054:
close to 1 have less of a smoothing effect and give greater weight to recent changes in the data, while values of
9132:
8793:
8538:
7909:
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closer to 0 have a greater smoothing effect and are less responsive to recent changes. In the limiting case with
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9183:
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8202:
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8049:
6586:
2885:
2718:, and the weights assigned to previous observations are proportional to the terms of the geometric progression
2197:
By direct substitution of the defining equation for simple exponential smoothing back into itself we find that
661:. Exponential smoothing was first suggested in the statistical literature without citation to previous work by
67:
8123:
7035:
6565:: the holtwinters module of the statsmodels package allow for simple, double and triple exponential smoothing.
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8977:
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past data points. Computationally speaking, they also differ in that moving average requires that the past
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is the sequence of best estimates of the linear trend that are superimposed on the seasonal changes, and
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in nature. Multiplicative seasonality can be represented as a constant factor, not an absolute amount.
2172:{\displaystyle {\text{SSE}}=\sum _{t=1}^{T}(y_{t}-{\hat {y}}_{t\mid t-1})^{2}=\sum _{t=1}^{T}e_{t}^{2}}
1567:
657:
community in the 1940s. Here, exponential smoothing is the application of the exponential, or
Poisson,
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2183:
675:
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If every month of
December we sell 10,000 more apartments than we do in November the seasonality is
9596:
9421:
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9051:
8736:
8701:
8665:
8450:
7892:
7801:
7760:
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6033:
377:
66:'s use of recursive exponential window functions in convolutions from the 19th century, as well as
6928:
6792:
4630:
in the cycle that the observations take on. As a rule of thumb, a minimum of two full seasons (or
653:
as an extension of a numerical analysis technique from the 17th century, and later adopted by the
9330:
8943:
8883:
8820:
8458:
8442:
8180:
8042:
8032:
7882:
7796:
671:
7172:
5973:{\displaystyle A_{j}={\frac {\sum _{i=1}^{L}x_{L(j-1)+i}}{L}}\quad {\text{for }}j=1,2,\ldots ,N}
650:
63:
9368:
9298:
9091:
9028:
8783:
8670:
7667:
7564:
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7350:
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1884:
1284:
4725:
1544:
9578:
9393:
9335:
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9104:
8906:
8632:
8516:
8375:
8367:
8257:
8249:
8064:
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7897:
7862:
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7406:
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3090:
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1404:
1201:
1177:
1153:
1077:
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1037:
1017:
997:
977:
940:
830:
39:
7006:
Winters, P. R. (April 1960). "Forecasting Sales by
Exponentially Weighted Moving Averages".
6746:(JanuaryâMarch 2004). "Forecasting Trends and Seasonal by Exponentially Weighted Averages".
5291:
4363:
3566:
3271:
3123:
9626:
9316:
8891:
8840:
8816:
8778:
8696:
8675:
8627:
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8081:
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7993:
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4566:
4539:
4512:
4465:
3625:
3010:
2963:
2910:
2829:
2630:
1760:
1757:, the more sensitive your forecast will be on the selection of this initial smoother value
1680:
1653:
1384:
913:
886:
662:
617:
496:
135:
76:
7068:
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literature, the use of non-causal (symmetric) filters is commonplace, and the exponential
8:
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2937:
409:
353:
6793:"NIST/SEMATECH e-Handbook of Statistical Methods, 6.4.3.1. Single Exponential Smoothing"
4774:. Triple exponential smoothing with multiplicative seasonality is given by the formulas
4633:
3258:{\displaystyle {\begin{aligned}s_{0}&=x_{0}\\b_{0}&=x_{1}-x_{0}\\\end{aligned}}}
1796:), but for the methods that follow there are usually more than one smoothing parameter.
9477:
9288:
9142:
9038:
8987:
8863:
8760:
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8721:
8498:
8232:
8215:
8175:
8086:
7981:
7943:
7914:
7874:
7834:
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7697:
7383:
7378:
7182:
Algorithms for
Unevenly Spaced Time Series: Moving Averages and Other Rolling Operators
6633:
6013:
5691:
5406:
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4613:
4593:
4492:
4442:
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3723:
3149:
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2017:
1997:
1922:
1334:
1097:
533:
469:
442:
2654:
becomes the weighted average of a greater and greater number of the past observations
1594:
1333:
of an exponential moving average is the amount of time for the smoothed response of a
9606:
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9383:
9353:
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7998:
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7687:
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6883:
6761:
6691:
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1124:
817:{\displaystyle s_{t}=\alpha x_{t}+(1-\alpha )s_{t-1}=s_{t-1}+\alpha (x_{t}-s_{t-1}).}
654:
563:
188:
109:
51:
1677:(the initial output of the exponential smoothing algorithm) is being initialized to
9513:
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47:
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is undefined (there is no estimation for time 0), and according to the definition
560:
The simple exponential smoothing is not able to predict what would be observed at
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8357:
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7953:
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7173:
The HoltâWinters
Approach to Exponential Smoothing: 50 Years Old and Going Strong
6844:Äisar, P., & Äisar, S. M. (2011). "Optimization methods of EWMA statistics."
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4653:
periods) of historical data is needed to initialize a set of seasonal factors.
132:, and the output of the exponential smoothing algorithm is commonly written as
6731:(1957). "Forecasting Trends and Seasonal by Exponentially Weighted Averages".
2832:, so this is where the name for this smoothing method originated according to
9620:
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9033:
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2814:{\displaystyle 1,(1-\alpha ),(1-\alpha )^{2},\ldots ,(1-\alpha )^{n},\ldots }
1330:
1195:
27:
6860:
7.1 Simple exponential smoothing | Forecasting: Principles and
Practice
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smoothing models and ARIMA models with a range of nonseasonal and seasonal
1034:= 1 the smoothing output series is just the current observation. Values of
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31:
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is a matter of preference. An option other than the one listed above is
8262:
7742:
7442:
7373:
7323:
7298:
7218:
6953:
6815:
2833:
211:, the simplest form of exponential smoothing is given by the formulas:
1014:
actually reduce the level of smoothing, and in the limiting case with
8415:
8267:
7887:
7682:
7594:
7579:
7574:
7539:
7143:"Excel 2016 Forecasting Functions | Real Statistics Using Excel"
1381:
of the original signal. The relationship between this time constant,
1094:= 0, the output series is just flat or a constant as the observation
165:, which may be regarded as a best estimate of what the next value of
7159:
Lecture notes on exponential smoothing (Robert Nau, Duke
University)
6681:
6060:
Triple exponential smoothing with additive seasonality is given by:
4563:
is the sequence of seasonal correction factors. We wish to estimate
681:
The simplest form of exponential smoothing is given by the formula:
7931:
7549:
7426:
7421:
7416:
6980:"Time series Forecasting using HoltâWinters Exponential Smoothing"
649:
The use of the exponential window function is first attributed to
9436:
9137:
6858:
611:
9358:
8339:
8313:
8293:
7544:
7335:
7129:"LibreOffice 5.2: Release Notes â the Document Foundation Wiki"
6907:
3840:, which is well defined, thus further values can be evaluated.
2907:
Again, the raw data sequence of observations is represented by
607:
4328:
2896:
Simple exponential smoothing does not do well when there is a
1313:
This simple form of exponential smoothing is also known as an
7187:
6717:. Cambridge, Massachusetts: Arthur D. Little Inc. p. 15.
6592:
6519:
5708:
is the number of complete cycles present in your data, then:
5201:
2891:
59:
6778:
Smoothing
Forecasting and Prediction of Discrete Time Series
7278:
7177:
Foresight: The International Journal of Applied Forecasting
6677:
6675:
6569:
4489:
represent the smoothed value of the constant part for time
185:
will be. When the sequence of observations begins at time
68:
Kolmogorov and Zurbenko's use of recursive moving averages
6550:
1919:(the one-step-ahead within-sample forecast errors) where
1531:{\displaystyle \tau =-{\frac {\Delta T}{\ln(1-\alpha )}}}
557:
is revealed, showing how exponential smoothing is named.
6672:
3166:. Double exponential smoothing is given by the formulas
1631:{\displaystyle \alpha \approx {\frac {\Delta T}{\tau }}}
910:
is a simple weighted average of the current observation
5617:
Setting the initial estimates for the seasonal indices
644:
641:
as the sequence of best estimates of the linear trend.
3746:
2627:
In other words, as time passes the smoothed statistic
1952:
1925:
1887:
1813:
1641:
1127:
1100:
614:
can be used for the prediction due to the presence of
592:
566:
536:
499:
472:
445:
412:
380:
356:
191:
171:
138:
112:
79:
16:
Generates a forecast of future values of a time series
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2043:
2020:
2000:
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1710:
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1606:
1570:
1547:
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1407:
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1343:
1287:
1224:
1204:
1180:
1156:
1080:
1060:
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1020:
1000:
994:
here is something of a misnomer, as larger values of
980:
943:
916:
889:
857:
833:
690:
620:
220:
9543:
9100:
Autoregressive conditional heteroskedasticity (ARCH)
7061:"ets {forecast} | inside-R | A Community Site for R"
1317:(EWMA). Technically it can also be classified as an
1150:
There is no formally correct procedure for choosing
6835:"Production and Operations Analysis" Nahmias. 2009.
5403:The general formula for the initial trend estimate
2884:(IIR) filter and moving average is equivalent to a
1800:method is to estimate them from the observed data.
1281:example, a constant signal will take approximately
527:
8562:
7001:
6999:
6539:
6049:
6022:
6002:
5972:
5842:
5700:
5680:
5636:
5606:
5415:
5388:
5356:
5332:
5300:
5276:
5244:
5221:
4766:
4746:
4714:
4681:
4645:
4622:
4602:
4582:
4555:
4528:
4501:
4481:
4451:
4428:
4408:
4382:
4317:
4134:
3801:
3781:
3732:
3709:
3641:
3607:
3575:
3551:
3519:
3496:
3286:
3257:
3158:
3138:
3112:
3079:
3046:
3026:
2999:
2979:
2952:
2926:
2813:
2710:
2646:
2616:
2171:
2026:
2006:
1986:
1938:
1911:
1873:
1776:
1749:
1729:
1696:
1669:
1630:
1585:
1556:
1530:
1469:
1413:
1393:
1373:
1301:
1269:
1210:
1186:
1162:
1139:
1113:
1086:
1066:
1046:
1026:
1006:
986:
962:
929:
902:
875:
839:
816:
633:
598:
578:
549:
518:
485:
458:
431:
398:
362:
339:
203:
177:
157:
124:
98:
6658:"NIST/SEMATECH e-Handbook of Statistical Methods"
2839:
2189:
9618:
4656:The output of the algorithm is again written as
3054:. The output of the algorithm is now written as
1595:the Taylor expansion of the exponential function
8648:Multivariate adaptive regression splines (MARS)
6996:
6682:Oppenheim, Alan V.; Schafer, Ronald W. (1975).
2711:{\displaystyle s_{t-1},\ldots ,s_{t-n},\ldots }
1874:{\textstyle e_{t}=y_{t}-{\hat {y}}_{t\mid t-1}}
70:from their studies of turbulence in the 1940s.
6585:values, and selects the model with the lowest
73:The raw data sequence is often represented by
9529:
7203:
1470:{\displaystyle \alpha =1-e^{-\Delta T/\tau }}
1321:(ARIMA) (0,1,1) model with no constant term.
43:often used for analysis of time-series data.
6954:"Averaging and Exponential Smoothing Models"
6816:"Averaging and Exponential Smoothing Models"
1121:at the beginning of the smoothening process
513:
500:
152:
139:
93:
80:
6904:"Model: Second-Order Exponential Smoothing"
6714:Exponential Smoothing for Predicting Demand
4329:Triple exponential smoothing (Holt Winters)
2014:and a variable as the prediction result at
9536:
9522:
7248:
7210:
7196:
6851:
4416:with a cycle of seasonal change of length
3710:{\displaystyle F_{t+m}=s_{t}+m\cdot b_{t}}
3034:is our best estimate of the trend at time
2892:Double exponential smoothing (Holt linear)
7861:
2987:to represent the smoothed value for time
1367:
883:. In other words, the smoothed statistic
6878:(7th ed.). Waveland Press. p.
6873:
1319:autoregressive integrated moving average
1198:might be used to determine the value of
528:exponentially decaying weighting factors
7005:
6929:"6.4.3.3. Double Exponential Smoothing"
6785:
9619:
9174:KaplanâMeier estimator (product limit)
6781:. Englewood Cliffs, NJ: Prentice-Hall.
6652:
6650:
6648:
6551:Implementations in statistics packages
2865:data points, or the data point at lag
9517:
9247:
8814:
8561:
7860:
7630:
7247:
7191:
6874:Nahmias, Steven; Olsen, Tava Lennon.
6774:
6710:
3782:{\textstyle {\frac {x_{n}-x_{0}}{n}}}
1374:{\displaystyle 1-1/e\approx 63.2\,\%}
1315:exponentially weighted moving average
46:Exponential smoothing is one of many
9484:
9184:Accelerated failure time (AFT) model
6749:International Journal of Forecasting
6742:
6727:
1218:for which the sum of the quantities
937:and the previous smoothed statistic
645:Basic (simple) exponential smoothing
466:continuously so that the formula of
9496:
8779:Analysis of variance (ANOVA, anova)
7631:
7091:"Comparing HoltWinters() and ets()"
6977:
6733:Office of Naval Research Memorandum
6645:
6618:Autoregressive moving average model
5389:{\displaystyle 0\leq \gamma \leq 1}
5277:{\displaystyle 0\leq \alpha \leq 1}
3552:{\displaystyle 0\leq \alpha \leq 1}
1987:{\textstyle {\hat {y}}_{t\mid t-1}}
1807:(SSE). The errors are specified as
1642:Choosing the initial smoothed value
1270:{\displaystyle (s_{t}-x_{t+1})^{2}}
876:{\displaystyle 0\leq \alpha \leq 1}
50:commonly applied to smooth data in
13:
8874:CochranâMantelâHaenszel statistics
7500:Pearson product-moment correlation
7168:The Wolfram Demonstrations Project
6876:Production and Operations Analysis
6624:Errors and residuals in statistics
5333:{\displaystyle 0\leq \beta \leq 1}
3608:{\displaystyle 0\leq \beta \leq 1}
1994:are a variable to be predicted at
1616:
1571:
1548:
1496:
1451:
1368:
14:
9638:
7152:
4754:based on the raw data up to time
3146:based on the raw data up to time
1586:{\displaystyle \Delta T\ll \tau }
9495:
9483:
9471:
9458:
9457:
9248:
6762:10.1016/j.ijforecast.2003.09.015
5398:seasonal change smoothing factor
1324:
24:exponential moving average (EMA)
9589:Associative (causal) forecasts
9133:Least-squares spectral analysis
7135:
7121:
7109:
7083:
7053:
7028:
6971:
6946:
6921:
6896:
6867:
6813:
5937:
5807:
5681:{\displaystyle i=1,2,\ldots ,L}
3649:is given by the approximation:
1787:
493:is fully expressed in terms of
323:
8114:Mean-unbiased minimum-variance
7217:
6838:
6829:
6807:
6775:Brown, Robert Goodell (1963).
6768:
6721:
6704:
6587:Bayesian Information Criterion
6515:
6503:
6405:
6393:
6387:
6336:
6293:
6281:
6275:
6243:
6216:
6178:
6175:
6163:
6157:
6125:
5920:
5908:
5784:
5772:
5197:
5185:
5159:
5130:
5084:
5072:
5002:
4990:
4984:
4952:
4925:
4887:
4884:
4872:
4689:, an estimate of the value of
4305:
4273:
4167:, the estimated trend at time
4154:, the estimated level at time
4050:
4038:
3973:
3961:
3471:
3459:
3453:
3421:
3394:
3356:
3353:
3341:
3087:, an estimate of the value of
2904:One method, works as follows:
2888:with equal weighting factors.
2886:finite impulse response filter
2840:Comparison with moving average
2828:is the discrete version of an
2796:
2783:
2765:
2752:
2746:
2734:
2588:
2575:
2542:
2529:
2495:
2482:
2454:
2441:
2419:
2407:
2351:
2338:
2316:
2304:
2256:
2244:
2121:
2096:
2073:
1960:
1847:
1522:
1510:
1258:
1225:
808:
776:
732:
720:
665:in 1956, and then expanded by
399:{\textstyle 0<\alpha <1}
301:
289:
1:
9427:Geographic information system
8643:Simultaneous equations models
6050:{\displaystyle j^{\text{th}}}
62:. This method is preceded by
9574:Decomposition of time series
8610:Coefficient of determination
8221:Uniformly most powerful test
1401:, and the smoothing factor,
612:triple exponential smoothing
608:double exponential smoothing
586:based on the raw data up to
7:
9179:Proportional hazards models
9123:Spectral density estimation
9105:Vector autoregression (VAR)
8539:Maximum posterior estimator
7771:Randomized controlled trial
7036:"R: HoltâWinters Filtering"
6846:Acta Polytechnica Hungarica
6611:
5688:is a bit more involved. If
1421:, is given by the formula:
34:data using the exponential
10:
9643:
9555:Historical data forecasts
8939:Multivariate distributions
7359:Average absolute deviation
3720:Setting the initial value
1912:{\textstyle t=1,\ldots ,T}
9587:
9553:
9453:
9407:
9344:
9297:
9260:
9256:
9243:
9215:
9197:
9164:
9155:
9113:
9060:
9021:
8970:
8961:
8927:Structural equation model
8882:
8839:
8835:
8810:
8769:
8735:
8689:
8656:
8618:
8585:
8581:
8557:
8497:
8406:
8325:
8289:
8280:
8263:Score/Lagrange multiplier
8248:
8201:
8146:
8072:
8063:
7873:
7869:
7856:
7815:
7789:
7741:
7696:
7678:Sample size determination
7643:
7639:
7626:
7530:
7485:
7459:
7441:
7397:
7349:
7269:
7260:
7256:
7243:
7225:
6711:Brown, Robert G. (1956).
6684:Digital Signal Processing
2882:infinite-impulse response
1302:{\displaystyle 3/\alpha }
676:infinite impulse response
58:to remove high-frequency
9597:Simple linear regression
9422:Environmental statistics
8944:Elliptical distributions
8737:Generalized linear model
8666:Simple linear regression
8436:HodgesâLehmann estimator
7893:Probability distribution
7802:Stochastic approximation
7364:Coefficient of variation
6639:
6010:is the average value of
4747:{\displaystyle t+m>0}
1557:{\displaystyle \Delta T}
30:technique for smoothing
9082:Cross-correlation (XCF)
8690:Non-standard predictors
8124:LehmannâScheffĂ© theorem
7797:Adaptive clinical trial
7175:by Paul Goodwin (2010)
6848:, 8(5), 73â87. Page 78.
5357:{\displaystyle \gamma }
5245:{\displaystyle \alpha }
4715:{\displaystyle x_{t+m}}
4682:{\displaystyle F_{t+m}}
3520:{\displaystyle \alpha }
3113:{\displaystyle x_{t+m}}
3080:{\displaystyle F_{t+m}}
1750:{\displaystyle \alpha }
1730:{\displaystyle s_{t-1}}
1414:{\displaystyle \alpha }
1211:{\displaystyle \alpha }
1196:method of least squares
1187:{\displaystyle \alpha }
1163:{\displaystyle \alpha }
1087:{\displaystyle \alpha }
1067:{\displaystyle \alpha }
1047:{\displaystyle \alpha }
1027:{\displaystyle \alpha }
1007:{\displaystyle \alpha }
987:{\displaystyle \alpha }
963:{\displaystyle s_{t-1}}
840:{\displaystyle \alpha }
672:finite impulse response
9478:Mathematics portal
9299:Engineering statistics
9207:NelsonâAalen estimator
8784:Analysis of covariance
8671:Ordinary least squares
8595:Pearson product-moment
7999:Statistical functional
7910:Empirical distribution
7743:Controlled experiments
7472:Frequency distribution
7250:Descriptive statistics
6541:
6051:
6024:
6004:
5974:
5899:
5844:
5761:
5702:
5682:
5638:
5608:
5417:
5390:
5358:
5342:trend smoothing factor
5334:
5302:
5301:{\displaystyle \beta }
5278:
5246:
5223:
4768:
4748:
4716:
4683:
4647:
4624:
4604:
4584:
4557:
4530:
4503:
4483:
4453:
4430:
4410:
4384:
4383:{\displaystyle x_{t},}
4319:
4136:
3803:
3783:
3734:
3711:
3643:
3617:trend smoothing factor
3609:
3577:
3576:{\displaystyle \beta }
3553:
3521:
3498:
3288:
3287:{\displaystyle t>0}
3259:
3160:
3140:
3139:{\displaystyle m>0}
3114:
3081:
3048:
3028:
3001:
2981:
2954:
2928:
2853: + 1) where
2815:
2712:
2648:
2618:
2186:tool to perform this.
2173:
2153:
2072:
2028:
2008:
1988:
1940:
1913:
1875:
1778:
1751:
1731:
1698:
1671:
1632:
1587:
1558:
1532:
1471:
1415:
1395:
1375:
1303:
1271:
1212:
1188:
1164:
1141:
1115:
1088:
1068:
1048:
1028:
1008:
988:
964:
931:
904:
877:
841:
818:
635:
600:
580:
551:
520:
519:{\textstyle \{x_{t}\}}
487:
460:
433:
400:
364:
341:
205:
179:
159:
158:{\textstyle \{s_{t}\}}
126:
100:
99:{\textstyle \{x_{t}\}}
9564:Exponential smoothing
9394:Population statistics
9336:System identification
9070:Autocorrelation (ACF)
8998:Exponential smoothing
8912:Discriminant analysis
8907:Canonical correlation
8771:Partition of variance
8633:Regression validation
8477:(JonckheereâTerpstra)
8376:Likelihood-ratio test
8065:Frequentist inference
7977:Locationâscale family
7898:Sampling distribution
7863:Statistical inference
7830:Cross-sectional study
7817:Observational studies
7776:Randomized experiment
7605:Stem-and-leaf display
7407:Central limit theorem
6978:Kalehar, Prajakta S.
6542:
6052:
6025:
6005:
6003:{\displaystyle A_{j}}
5975:
5879:
5845:
5741:
5703:
5683:
5639:
5637:{\displaystyle c_{i}}
5609:
5418:
5391:
5359:
5335:
5303:
5286:data smoothing factor
5279:
5247:
5224:
4769:
4749:
4717:
4684:
4648:
4625:
4605:
4585:
4583:{\displaystyle c_{t}}
4558:
4556:{\displaystyle c_{t}}
4531:
4529:{\displaystyle b_{t}}
4504:
4484:
4482:{\displaystyle s_{t}}
4454:
4431:
4411:
4385:
4320:
4137:
3804:
3784:
3735:
3712:
3644:
3642:{\displaystyle x_{t}}
3610:
3578:
3561:data smoothing factor
3554:
3522:
3499:
3289:
3260:
3161:
3141:
3115:
3082:
3049:
3029:
3027:{\displaystyle b_{t}}
3002:
2982:
2980:{\displaystyle s_{t}}
2955:
2929:
2927:{\displaystyle x_{t}}
2826:geometric progression
2816:
2713:
2649:
2647:{\displaystyle s_{t}}
2619:
2174:
2133:
2052:
2029:
2009:
1989:
1941:
1914:
1876:
1805:sum of squared errors
1779:
1777:{\displaystyle s_{0}}
1752:
1732:
1699:
1697:{\displaystyle x_{0}}
1672:
1670:{\displaystyle s_{0}}
1633:
1588:
1559:
1533:
1472:
1416:
1396:
1394:{\displaystyle \tau }
1376:
1304:
1272:
1213:
1189:
1165:
1142:
1116:
1089:
1069:
1049:
1029:
1009:
989:
965:
932:
930:{\displaystyle x_{t}}
905:
903:{\displaystyle s_{t}}
878:
842:
819:
636:
634:{\displaystyle b_{t}}
601:
581:
552:
521:
488:
461:
434:
401:
365:
342:
206:
180:
160:
127:
101:
40:simple moving average
20:Exponential smoothing
9317:Probabilistic design
8902:Principal components
8745:Exponential families
8697:Nonlinear regression
8676:General linear model
8638:Mixed effects models
8628:Errors and residuals
8605:Confounding variable
8507:Bayesian probability
8485:Van der Waerden test
8475:Ordered alternative
8240:Multiple comparisons
8119:RaoâBlackwellization
8082:Estimating equations
8038:Statistical distance
7756:Factorial experiment
7289:Arithmetic-Geometric
7022:10.1287/mnsc.6.3.324
6067:
6057:cycle of your data.
6034:
6014:
5987:
5860:
5715:
5692:
5648:
5621:
5430:
5407:
5368:
5348:
5312:
5292:
5256:
5236:
4781:
4758:
4726:
4693:
4660:
4634:
4614:
4594:
4567:
4540:
4513:
4493:
4466:
4443:
4420:
4394:
4364:
4178:
3850:
3793:
3744:
3724:
3656:
3626:
3587:
3567:
3531:
3511:
3301:
3272:
3173:
3150:
3124:
3091:
3058:
3038:
3011:
2991:
2964:
2938:
2934:, beginning at time
2911:
2830:exponential function
2725:
2658:
2631:
2204:
2190:"Exponential" naming
2041:
2018:
1998:
1950:
1923:
1885:
1811:
1761:
1741:
1708:
1681:
1654:
1648:the definition above
1604:
1568:
1545:
1481:
1428:
1405:
1385:
1341:
1285:
1222:
1202:
1178:
1154:
1125:
1098:
1078:
1058:
1038:
1018:
998:
978:
941:
914:
887:
855:
831:
688:
663:Robert Goodell Brown
618:
590:
564:
534:
497:
470:
443:
439:is substituted into
432:{\textstyle s_{t-1}}
410:
378:
363:{\textstyle \alpha }
354:
218:
189:
169:
136:
110:
77:
9602:Regression analysis
9389:Official statistics
9312:Methods engineering
8993:Seasonal adjustment
8761:Poisson regressions
8681:Bayesian regression
8620:Regression analysis
8600:Partial correlation
8572:Regression analysis
8171:Prediction interval
8166:Likelihood interval
8156:Confidence interval
8148:Interval estimation
8109:Unbiased estimators
7927:Model specification
7807:Up-and-down designs
7495:Partial correlation
7451:Index of dispersion
7369:Interquartile range
4409:{\displaystyle t=0}
4354:Hadamard conjecture
4304:
4288:
4233:
4217:
4071:
4034:
4011:
3994:
3937:
3903:
3869:
3622:To forecast beyond
2953:{\displaystyle t=0}
2168:
1194:. For example, the
9409:Spatial statistics
9289:Medical statistics
9189:First hitting time
9143:Whittle likelihood
8794:Degrees of freedom
8789:Multivariate ANOVA
8722:Heteroscedasticity
8534:Bayesian estimator
8499:Bayesian inference
8348:KolmogorovâSmirnov
8233:Randomization test
8203:Testing hypotheses
8176:Tolerance interval
8087:Maximum likelihood
7982:Exponential family
7915:Density estimation
7875:Statistical theory
7835:Natural experiment
7781:Scientific control
7698:Survey methodology
7384:Standard deviation
7009:Management Science
6634:Continued fraction
6595:: tssmooth command
6537:
6535:
6047:
6020:
6000:
5970:
5840:
5698:
5678:
5634:
5604:
5602:
5413:
5386:
5354:
5330:
5298:
5274:
5242:
5219:
5217:
4764:
4744:
4712:
4679:
4646:{\displaystyle 2L}
4643:
4620:
4600:
4580:
4553:
4526:
4499:
4479:
4449:
4426:
4406:
4390:beginning at time
4380:
4315:
4313:
4292:
4276:
4221:
4205:
4132:
4130:
4053:
4022:
3999:
3976:
3925:
3891:
3857:
3799:
3779:
3730:
3707:
3639:
3605:
3573:
3549:
3517:
3494:
3492:
3284:
3255:
3253:
3156:
3136:
3110:
3077:
3044:
3024:
2997:
2977:
2950:
2924:
2811:
2708:
2644:
2614:
2612:
2169:
2154:
2024:
2004:
1984:
1939:{\textstyle y_{t}}
1936:
1909:
1871:
1774:
1747:
1727:
1694:
1667:
1628:
1583:
1554:
1528:
1467:
1411:
1391:
1371:
1335:unit step function
1299:
1267:
1208:
1184:
1160:
1137:
1114:{\textstyle x_{0}}
1111:
1084:
1064:
1044:
1024:
1004:
984:
960:
927:
900:
873:
837:
814:
631:
596:
576:
550:{\textstyle x_{t}}
547:
516:
486:{\textstyle s_{t}}
483:
459:{\textstyle s_{t}}
456:
429:
396:
360:
337:
335:
201:
175:
155:
122:
106:beginning at time
96:
9614:
9613:
9607:Econometric model
9511:
9510:
9449:
9448:
9445:
9444:
9384:National accounts
9354:Actuarial science
9346:Social statistics
9239:
9238:
9235:
9234:
9231:
9230:
9166:Survival function
9151:
9150:
9013:Granger causality
8854:Contingency table
8829:Survival analysis
8806:
8805:
8802:
8801:
8658:Linear regression
8553:
8552:
8549:
8548:
8524:Credible interval
8493:
8492:
8276:
8275:
8092:Method of moments
7961:Parametric family
7922:Statistical model
7852:
7851:
7848:
7847:
7766:Random assignment
7688:Statistical power
7622:
7621:
7618:
7617:
7467:Contingency table
7437:
7436:
7304:Generalized/power
7184:by Andreas Eckner
6044:
6023:{\displaystyle x}
5941:
5935:
5811:
5805:
5739:
5701:{\displaystyle N}
5593:
5546:
5505:
5462:
5416:{\displaystyle b}
5067:
4867:
4767:{\displaystyle t}
4623:{\displaystyle L}
4603:{\displaystyle t}
4502:{\displaystyle t}
4452:{\displaystyle L}
4429:{\displaystyle L}
4271:
3802:{\displaystyle n}
3777:
3733:{\displaystyle b}
3159:{\displaystyle t}
3047:{\displaystyle t}
3000:{\displaystyle t}
2874:signal processing
2099:
2047:
2027:{\displaystyle t}
2007:{\displaystyle t}
1963:
1850:
1626:
1593:) then, by using
1526:
674:(FIR) filters to
655:signal processing
530:on each raw data
52:signal processing
38:. Whereas in the
9634:
9538:
9531:
9524:
9515:
9514:
9499:
9498:
9487:
9486:
9476:
9475:
9461:
9460:
9364:Crime statistics
9258:
9257:
9245:
9244:
9162:
9161:
9128:Fourier analysis
9115:Frequency domain
9095:
9042:
9008:Structural break
8968:
8967:
8917:Cluster analysis
8864:Log-linear model
8837:
8836:
8812:
8811:
8753:
8727:Homoscedasticity
8583:
8582:
8559:
8558:
8478:
8470:
8462:
8461:(KruskalâWallis)
8446:
8431:
8386:Cross validation
8371:
8353:AndersonâDarling
8300:
8287:
8286:
8258:Likelihood-ratio
8250:Parametric tests
8228:Permutation test
8211:1- & 2-tails
8102:Minimum distance
8074:Point estimation
8070:
8069:
8021:Optimal decision
7972:
7871:
7870:
7858:
7857:
7840:Quasi-experiment
7790:Adaptive designs
7641:
7640:
7628:
7627:
7505:Rank correlation
7267:
7266:
7258:
7257:
7245:
7244:
7212:
7205:
7198:
7189:
7188:
7166:by Jon McLoone,
7147:
7146:
7139:
7133:
7132:
7125:
7119:
7113:
7107:
7106:
7104:
7102:
7087:
7081:
7080:
7078:
7076:
7067:. Archived from
7057:
7051:
7050:
7048:
7046:
7032:
7026:
7025:
7003:
6994:
6993:
6991:
6989:
6984:
6975:
6969:
6968:
6966:
6964:
6950:
6944:
6943:
6941:
6939:
6925:
6919:
6918:
6916:
6914:
6900:
6894:
6893:
6871:
6865:
6864:
6855:
6849:
6842:
6836:
6833:
6827:
6826:
6824:
6822:
6811:
6805:
6804:
6802:
6800:
6789:
6783:
6782:
6772:
6766:
6765:
6744:Holt, Charles C.
6740:
6729:Holt, Charles C.
6725:
6719:
6718:
6708:
6702:
6701:
6679:
6670:
6669:
6667:
6665:
6654:
6546:
6544:
6543:
6538:
6536:
6529:
6528:
6527:
6526:
6476:
6475:
6460:
6459:
6443:
6442:
6423:
6422:
6386:
6385:
6367:
6366:
6348:
6347:
6325:
6324:
6311:
6310:
6274:
6273:
6255:
6254:
6232:
6231:
6215:
6214:
6196:
6195:
6156:
6155:
6137:
6136:
6114:
6113:
6100:
6099:
6083:
6082:
6056:
6054:
6053:
6048:
6046:
6045:
6042:
6029:
6027:
6026:
6021:
6009:
6007:
6006:
6001:
5999:
5998:
5979:
5977:
5976:
5971:
5942:
5939:
5936:
5931:
5930:
5929:
5898:
5893:
5877:
5872:
5871:
5849:
5847:
5846:
5841:
5812:
5809:
5806:
5804:
5803:
5794:
5793:
5763:
5760:
5755:
5740:
5732:
5727:
5726:
5707:
5705:
5704:
5699:
5687:
5685:
5684:
5679:
5643:
5641:
5640:
5635:
5633:
5632:
5613:
5611:
5610:
5605:
5603:
5599:
5595:
5594:
5589:
5588:
5587:
5575:
5574:
5558:
5547:
5542:
5541:
5540:
5528:
5527:
5511:
5506:
5501:
5500:
5499:
5487:
5486:
5470:
5463:
5455:
5446:
5445:
5422:
5420:
5419:
5414:
5395:
5393:
5392:
5387:
5363:
5361:
5360:
5355:
5339:
5337:
5336:
5331:
5307:
5305:
5304:
5299:
5283:
5281:
5280:
5275:
5251:
5249:
5248:
5243:
5228:
5226:
5225:
5220:
5218:
5211:
5210:
5209:
5208:
5158:
5157:
5142:
5141:
5122:
5121:
5102:
5101:
5068:
5066:
5065:
5056:
5055:
5046:
5034:
5033:
5020:
5019:
4983:
4982:
4964:
4963:
4941:
4940:
4924:
4923:
4905:
4904:
4868:
4866:
4865:
4850:
4849:
4840:
4828:
4827:
4814:
4813:
4797:
4796:
4773:
4771:
4770:
4765:
4753:
4751:
4750:
4745:
4721:
4719:
4718:
4713:
4711:
4710:
4688:
4686:
4685:
4680:
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4508:
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4505:
4500:
4488:
4486:
4485:
4480:
4478:
4477:
4458:
4456:
4455:
4450:
4435:
4433:
4432:
4427:
4415:
4413:
4412:
4407:
4389:
4387:
4386:
4381:
4376:
4375:
4324:
4322:
4321:
4316:
4314:
4300:
4284:
4272:
4270:
4256:
4247:
4246:
4229:
4213:
4194:
4193:
4141:
4139:
4138:
4133:
4131:
4124:
4123:
4108:
4107:
4091:
4090:
4067:
4030:
4007:
3990:
3957:
3956:
3933:
3920:
3919:
3899:
3886:
3885:
3865:
3808:
3806:
3805:
3800:
3788:
3786:
3785:
3780:
3778:
3773:
3772:
3771:
3759:
3758:
3748:
3739:
3737:
3736:
3731:
3716:
3714:
3713:
3708:
3706:
3705:
3687:
3686:
3674:
3673:
3648:
3646:
3645:
3640:
3638:
3637:
3614:
3612:
3611:
3606:
3582:
3580:
3579:
3574:
3558:
3556:
3555:
3550:
3526:
3524:
3523:
3518:
3503:
3501:
3500:
3495:
3493:
3489:
3488:
3452:
3451:
3433:
3432:
3410:
3409:
3393:
3392:
3374:
3373:
3337:
3336:
3317:
3316:
3293:
3291:
3290:
3285:
3264:
3262:
3261:
3256:
3254:
3250:
3249:
3237:
3236:
3220:
3219:
3206:
3205:
3189:
3188:
3165:
3163:
3162:
3157:
3145:
3143:
3142:
3137:
3119:
3117:
3116:
3111:
3109:
3108:
3086:
3084:
3083:
3078:
3076:
3075:
3053:
3051:
3050:
3045:
3033:
3031:
3030:
3025:
3023:
3022:
3006:
3004:
3003:
2998:
2986:
2984:
2983:
2978:
2976:
2975:
2959:
2957:
2956:
2951:
2933:
2931:
2930:
2925:
2923:
2922:
2820:
2818:
2817:
2812:
2804:
2803:
2773:
2772:
2717:
2715:
2714:
2709:
2701:
2700:
2676:
2675:
2653:
2651:
2650:
2645:
2643:
2642:
2623:
2621:
2620:
2615:
2613:
2606:
2605:
2596:
2595:
2571:
2567:
2566:
2565:
2556:
2555:
2519:
2518:
2503:
2502:
2478:
2477:
2462:
2461:
2437:
2436:
2403:
2402:
2379:
2375:
2374:
2359:
2358:
2334:
2333:
2297:
2296:
2278:
2274:
2273:
2240:
2239:
2220:
2219:
2178:
2176:
2175:
2170:
2167:
2162:
2152:
2147:
2129:
2128:
2119:
2118:
2101:
2100:
2092:
2085:
2084:
2071:
2066:
2048:
2045:
2033:
2031:
2030:
2025:
2013:
2011:
2010:
2005:
1993:
1991:
1990:
1985:
1983:
1982:
1965:
1964:
1956:
1945:
1943:
1942:
1937:
1935:
1934:
1918:
1916:
1915:
1910:
1880:
1878:
1877:
1872:
1870:
1869:
1852:
1851:
1843:
1836:
1835:
1823:
1822:
1783:
1781:
1780:
1775:
1773:
1772:
1756:
1754:
1753:
1748:
1736:
1734:
1733:
1728:
1726:
1725:
1703:
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1700:
1695:
1693:
1692:
1676:
1674:
1673:
1668:
1666:
1665:
1637:
1635:
1634:
1629:
1627:
1622:
1614:
1592:
1590:
1589:
1584:
1563:
1561:
1560:
1555:
1537:
1535:
1534:
1529:
1527:
1525:
1502:
1494:
1476:
1474:
1473:
1468:
1466:
1465:
1461:
1420:
1418:
1417:
1412:
1400:
1398:
1397:
1392:
1380:
1378:
1377:
1372:
1357:
1308:
1306:
1305:
1300:
1295:
1276:
1274:
1273:
1268:
1266:
1265:
1256:
1255:
1237:
1236:
1217:
1215:
1214:
1209:
1193:
1191:
1190:
1185:
1169:
1167:
1166:
1161:
1146:
1144:
1143:
1140:{\textstyle t=0}
1138:
1120:
1118:
1117:
1112:
1110:
1109:
1093:
1091:
1090:
1085:
1073:
1071:
1070:
1065:
1053:
1051:
1050:
1045:
1033:
1031:
1030:
1025:
1013:
1011:
1010:
1005:
993:
991:
990:
985:
972:smoothing factor
969:
967:
966:
961:
959:
958:
936:
934:
933:
928:
926:
925:
909:
907:
906:
901:
899:
898:
882:
880:
879:
874:
849:smoothing factor
846:
844:
843:
838:
823:
821:
820:
815:
807:
806:
788:
787:
769:
768:
750:
749:
716:
715:
700:
699:
640:
638:
637:
632:
630:
629:
605:
603:
602:
597:
585:
583:
582:
579:{\textstyle t+m}
577:
556:
554:
553:
548:
546:
545:
525:
523:
522:
517:
512:
511:
492:
490:
489:
484:
482:
481:
465:
463:
462:
457:
455:
454:
438:
436:
435:
430:
428:
427:
405:
403:
402:
397:
372:smoothing factor
369:
367:
366:
361:
346:
344:
343:
338:
336:
319:
318:
285:
284:
265:
264:
251:
250:
234:
233:
210:
208:
207:
204:{\textstyle t=0}
202:
184:
182:
181:
176:
164:
162:
161:
156:
151:
150:
131:
129:
128:
125:{\textstyle t=0}
123:
105:
103:
102:
97:
92:
91:
56:low-pass filters
48:window functions
9642:
9641:
9637:
9636:
9635:
9633:
9632:
9631:
9617:
9616:
9615:
9610:
9583:
9549:
9542:
9512:
9507:
9470:
9441:
9403:
9340:
9326:quality control
9293:
9275:Clinical trials
9252:
9227:
9211:
9199:Hazard function
9193:
9147:
9109:
9093:
9056:
9052:BreuschâGodfrey
9040:
9017:
8957:
8932:Factor analysis
8878:
8859:Graphical model
8831:
8798:
8765:
8751:
8731:
8685:
8652:
8614:
8577:
8576:
8545:
8489:
8476:
8468:
8460:
8444:
8429:
8408:Rank statistics
8402:
8381:Model selection
8369:
8327:Goodness of fit
8321:
8298:
8272:
8244:
8197:
8142:
8131:Median unbiased
8059:
7970:
7903:Order statistic
7865:
7844:
7811:
7785:
7737:
7692:
7635:
7633:Data collection
7614:
7526:
7481:
7455:
7433:
7393:
7345:
7262:Continuous data
7252:
7239:
7221:
7216:
7155:
7150:
7141:
7140:
7136:
7127:
7126:
7122:
7118:in Stata manual
7114:
7110:
7100:
7098:
7089:
7088:
7084:
7074:
7072:
7071:on 16 July 2016
7059:
7058:
7054:
7044:
7042:
7034:
7033:
7029:
7004:
6997:
6987:
6985:
6982:
6976:
6972:
6962:
6960:
6952:
6951:
6947:
6937:
6935:
6927:
6926:
6922:
6912:
6910:
6902:
6901:
6897:
6890:
6872:
6868:
6857:
6856:
6852:
6843:
6839:
6834:
6830:
6820:
6818:
6812:
6808:
6798:
6796:
6791:
6790:
6786:
6773:
6769:
6726:
6722:
6709:
6705:
6698:
6680:
6673:
6663:
6661:
6656:
6655:
6646:
6642:
6614:
6605:Microsoft Excel
6553:
6534:
6533:
6522:
6518:
6484:
6480:
6471:
6467:
6455:
6451:
6444:
6432:
6428:
6425:
6424:
6412:
6408:
6375:
6371:
6356:
6352:
6343:
6339:
6326:
6320:
6316:
6313:
6312:
6300:
6296:
6263:
6259:
6250:
6246:
6233:
6227:
6223:
6220:
6219:
6204:
6200:
6185:
6181:
6145:
6141:
6132:
6128:
6115:
6109:
6105:
6102:
6101:
6095:
6091:
6084:
6078:
6074:
6070:
6068:
6065:
6064:
6041:
6037:
6035:
6032:
6031:
6015:
6012:
6011:
5994:
5990:
5988:
5985:
5984:
5938:
5904:
5900:
5894:
5883:
5878:
5876:
5867:
5863:
5861:
5858:
5857:
5808:
5799:
5795:
5768:
5764:
5762:
5756:
5745:
5731:
5722:
5718:
5716:
5713:
5712:
5693:
5690:
5689:
5649:
5646:
5645:
5628:
5624:
5622:
5619:
5618:
5601:
5600:
5583:
5579:
5564:
5560:
5559:
5557:
5536:
5532:
5517:
5513:
5512:
5510:
5495:
5491:
5476:
5472:
5471:
5469:
5468:
5464:
5454:
5447:
5441:
5437:
5433:
5431:
5428:
5427:
5408:
5405:
5404:
5369:
5366:
5365:
5349:
5346:
5345:
5313:
5310:
5309:
5293:
5290:
5289:
5257:
5254:
5253:
5237:
5234:
5233:
5216:
5215:
5204:
5200:
5166:
5162:
5153:
5149:
5137:
5133:
5123:
5111:
5107:
5104:
5103:
5091:
5087:
5061:
5057:
5051:
5047:
5045:
5035:
5029:
5025:
5022:
5021:
5009:
5005:
4972:
4968:
4959:
4955:
4942:
4936:
4932:
4929:
4928:
4913:
4909:
4894:
4890:
4855:
4851:
4845:
4841:
4839:
4829:
4823:
4819:
4816:
4815:
4809:
4805:
4798:
4792:
4788:
4784:
4782:
4779:
4778:
4759:
4756:
4755:
4727:
4724:
4723:
4700:
4696:
4694:
4691:
4690:
4667:
4663:
4661:
4658:
4657:
4635:
4632:
4631:
4615:
4612:
4611:
4595:
4592:
4591:
4574:
4570:
4568:
4565:
4564:
4547:
4543:
4541:
4538:
4537:
4520:
4516:
4514:
4511:
4510:
4494:
4491:
4490:
4473:
4469:
4467:
4464:
4463:
4444:
4441:
4440:
4421:
4418:
4417:
4395:
4392:
4391:
4371:
4367:
4365:
4362:
4361:
4331:
4312:
4311:
4296:
4280:
4260:
4255:
4248:
4242:
4238:
4235:
4234:
4225:
4209:
4195:
4189:
4185:
4181:
4179:
4176:
4175:
4166:
4153:
4129:
4128:
4119:
4115:
4103:
4099:
4092:
4080:
4076:
4073:
4072:
4057:
4026:
4012:
4003:
3996:
3995:
3980:
3952:
3948:
3938:
3929:
3922:
3921:
3915:
3911:
3904:
3895:
3888:
3887:
3881:
3877:
3870:
3861:
3853:
3851:
3848:
3847:
3839:
3832:
3825:
3818:
3794:
3791:
3790:
3767:
3763:
3754:
3750:
3749:
3747:
3745:
3742:
3741:
3725:
3722:
3721:
3701:
3697:
3682:
3678:
3663:
3659:
3657:
3654:
3653:
3633:
3629:
3627:
3624:
3623:
3588:
3585:
3584:
3568:
3565:
3564:
3532:
3529:
3528:
3512:
3509:
3508:
3491:
3490:
3478:
3474:
3441:
3437:
3428:
3424:
3411:
3405:
3401:
3398:
3397:
3382:
3378:
3363:
3359:
3332:
3328:
3318:
3312:
3308:
3304:
3302:
3299:
3298:
3273:
3270:
3269:
3252:
3251:
3245:
3241:
3232:
3228:
3221:
3215:
3211:
3208:
3207:
3201:
3197:
3190:
3184:
3180:
3176:
3174:
3171:
3170:
3151:
3148:
3147:
3125:
3122:
3121:
3098:
3094:
3092:
3089:
3088:
3065:
3061:
3059:
3056:
3055:
3039:
3036:
3035:
3018:
3014:
3012:
3009:
3008:
2992:
2989:
2988:
2971:
2967:
2965:
2962:
2961:
2939:
2936:
2935:
2918:
2914:
2912:
2909:
2908:
2894:
2878:window function
2842:
2799:
2795:
2768:
2764:
2726:
2723:
2722:
2690:
2686:
2665:
2661:
2659:
2656:
2655:
2638:
2634:
2632:
2629:
2628:
2611:
2610:
2601:
2597:
2591:
2587:
2561:
2557:
2545:
2541:
2508:
2504:
2498:
2494:
2467:
2463:
2457:
2453:
2426:
2422:
2398:
2394:
2393:
2389:
2377:
2376:
2364:
2360:
2354:
2350:
2323:
2319:
2292:
2288:
2276:
2275:
2263:
2259:
2235:
2231:
2221:
2215:
2211:
2207:
2205:
2202:
2201:
2192:
2163:
2158:
2148:
2137:
2124:
2120:
2102:
2091:
2090:
2089:
2080:
2076:
2067:
2056:
2044:
2042:
2039:
2038:
2019:
2016:
2015:
1999:
1996:
1995:
1966:
1955:
1954:
1953:
1951:
1948:
1947:
1930:
1926:
1924:
1921:
1920:
1886:
1883:
1882:
1853:
1842:
1841:
1840:
1831:
1827:
1818:
1814:
1812:
1809:
1808:
1790:
1768:
1764:
1762:
1759:
1758:
1742:
1739:
1738:
1715:
1711:
1709:
1706:
1705:
1688:
1684:
1682:
1679:
1678:
1661:
1657:
1655:
1652:
1651:
1644:
1615:
1613:
1605:
1602:
1601:
1569:
1566:
1565:
1546:
1543:
1542:
1503:
1495:
1493:
1482:
1479:
1478:
1457:
1447:
1443:
1429:
1426:
1425:
1406:
1403:
1402:
1386:
1383:
1382:
1353:
1342:
1339:
1338:
1327:
1291:
1286:
1283:
1282:
1261:
1257:
1245:
1241:
1232:
1228:
1223:
1220:
1219:
1203:
1200:
1199:
1179:
1176:
1175:
1155:
1152:
1151:
1126:
1123:
1122:
1105:
1101:
1099:
1096:
1095:
1079:
1076:
1075:
1059:
1056:
1055:
1039:
1036:
1035:
1019:
1016:
1015:
999:
996:
995:
979:
976:
975:
948:
944:
942:
939:
938:
921:
917:
915:
912:
911:
894:
890:
888:
885:
884:
856:
853:
852:
832:
829:
828:
796:
792:
783:
779:
758:
754:
739:
735:
711:
707:
695:
691:
689:
686:
685:
667:Charles C. Holt
659:window function
647:
625:
621:
619:
616:
615:
591:
588:
587:
565:
562:
561:
541:
537:
535:
532:
531:
507:
503:
498:
495:
494:
477:
473:
471:
468:
467:
450:
446:
444:
441:
440:
417:
413:
411:
408:
407:
379:
376:
375:
355:
352:
351:
334:
333:
308:
304:
280:
276:
266:
260:
256:
253:
252:
246:
242:
235:
229:
225:
221:
219:
216:
215:
190:
187:
186:
170:
167:
166:
146:
142:
137:
134:
133:
111:
108:
107:
87:
83:
78:
75:
74:
36:window function
17:
12:
11:
5:
9640:
9630:
9629:
9612:
9611:
9609:
9604:
9599:
9594:
9592:Moving average
9588:
9585:
9584:
9582:
9581:
9579:NaĂŻve approach
9576:
9571:
9569:Trend analysis
9566:
9561:
9559:Moving average
9554:
9551:
9550:
9541:
9540:
9533:
9526:
9518:
9509:
9508:
9506:
9505:
9493:
9481:
9467:
9454:
9451:
9450:
9447:
9446:
9443:
9442:
9440:
9439:
9434:
9429:
9424:
9419:
9413:
9411:
9405:
9404:
9402:
9401:
9396:
9391:
9386:
9381:
9376:
9371:
9366:
9361:
9356:
9350:
9348:
9342:
9341:
9339:
9338:
9333:
9328:
9319:
9314:
9309:
9303:
9301:
9295:
9294:
9292:
9291:
9286:
9281:
9272:
9270:Bioinformatics
9266:
9264:
9254:
9253:
9241:
9240:
9237:
9236:
9233:
9232:
9229:
9228:
9226:
9225:
9219:
9217:
9213:
9212:
9210:
9209:
9203:
9201:
9195:
9194:
9192:
9191:
9186:
9181:
9176:
9170:
9168:
9159:
9153:
9152:
9149:
9148:
9146:
9145:
9140:
9135:
9130:
9125:
9119:
9117:
9111:
9110:
9108:
9107:
9102:
9097:
9089:
9084:
9079:
9078:
9077:
9075:partial (PACF)
9066:
9064:
9058:
9057:
9055:
9054:
9049:
9044:
9036:
9031:
9025:
9023:
9022:Specific tests
9019:
9018:
9016:
9015:
9010:
9005:
9000:
8995:
8990:
8985:
8980:
8974:
8972:
8965:
8959:
8958:
8956:
8955:
8954:
8953:
8952:
8951:
8936:
8935:
8934:
8924:
8922:Classification
8919:
8914:
8909:
8904:
8899:
8894:
8888:
8886:
8880:
8879:
8877:
8876:
8871:
8869:McNemar's test
8866:
8861:
8856:
8851:
8845:
8843:
8833:
8832:
8808:
8807:
8804:
8803:
8800:
8799:
8797:
8796:
8791:
8786:
8781:
8775:
8773:
8767:
8766:
8764:
8763:
8747:
8741:
8739:
8733:
8732:
8730:
8729:
8724:
8719:
8714:
8709:
8707:Semiparametric
8704:
8699:
8693:
8691:
8687:
8686:
8684:
8683:
8678:
8673:
8668:
8662:
8660:
8654:
8653:
8651:
8650:
8645:
8640:
8635:
8630:
8624:
8622:
8616:
8615:
8613:
8612:
8607:
8602:
8597:
8591:
8589:
8579:
8578:
8575:
8574:
8569:
8563:
8555:
8554:
8551:
8550:
8547:
8546:
8544:
8543:
8542:
8541:
8531:
8526:
8521:
8520:
8519:
8514:
8503:
8501:
8495:
8494:
8491:
8490:
8488:
8487:
8482:
8481:
8480:
8472:
8464:
8448:
8445:(MannâWhitney)
8440:
8439:
8438:
8425:
8424:
8423:
8412:
8410:
8404:
8403:
8401:
8400:
8399:
8398:
8393:
8388:
8378:
8373:
8370:(ShapiroâWilk)
8365:
8360:
8355:
8350:
8345:
8337:
8331:
8329:
8323:
8322:
8320:
8319:
8311:
8302:
8290:
8284:
8282:Specific tests
8278:
8277:
8274:
8273:
8271:
8270:
8265:
8260:
8254:
8252:
8246:
8245:
8243:
8242:
8237:
8236:
8235:
8225:
8224:
8223:
8213:
8207:
8205:
8199:
8198:
8196:
8195:
8194:
8193:
8188:
8178:
8173:
8168:
8163:
8158:
8152:
8150:
8144:
8143:
8141:
8140:
8135:
8134:
8133:
8128:
8127:
8126:
8121:
8106:
8105:
8104:
8099:
8094:
8089:
8078:
8076:
8067:
8061:
8060:
8058:
8057:
8052:
8047:
8046:
8045:
8035:
8030:
8029:
8028:
8018:
8017:
8016:
8011:
8006:
7996:
7991:
7986:
7985:
7984:
7979:
7974:
7958:
7957:
7956:
7951:
7946:
7936:
7935:
7934:
7929:
7919:
7918:
7917:
7907:
7906:
7905:
7895:
7890:
7885:
7879:
7877:
7867:
7866:
7854:
7853:
7850:
7849:
7846:
7845:
7843:
7842:
7837:
7832:
7827:
7821:
7819:
7813:
7812:
7810:
7809:
7804:
7799:
7793:
7791:
7787:
7786:
7784:
7783:
7778:
7773:
7768:
7763:
7758:
7753:
7747:
7745:
7739:
7738:
7736:
7735:
7733:Standard error
7730:
7725:
7720:
7719:
7718:
7713:
7702:
7700:
7694:
7693:
7691:
7690:
7685:
7680:
7675:
7670:
7665:
7663:Optimal design
7660:
7655:
7649:
7647:
7637:
7636:
7624:
7623:
7620:
7619:
7616:
7615:
7613:
7612:
7607:
7602:
7597:
7592:
7587:
7582:
7577:
7572:
7567:
7562:
7557:
7552:
7547:
7542:
7536:
7534:
7528:
7527:
7525:
7524:
7519:
7518:
7517:
7512:
7502:
7497:
7491:
7489:
7483:
7482:
7480:
7479:
7474:
7469:
7463:
7461:
7460:Summary tables
7457:
7456:
7454:
7453:
7447:
7445:
7439:
7438:
7435:
7434:
7432:
7431:
7430:
7429:
7424:
7419:
7409:
7403:
7401:
7395:
7394:
7392:
7391:
7386:
7381:
7376:
7371:
7366:
7361:
7355:
7353:
7347:
7346:
7344:
7343:
7338:
7333:
7332:
7331:
7326:
7321:
7316:
7311:
7306:
7301:
7296:
7294:Contraharmonic
7291:
7286:
7275:
7273:
7264:
7254:
7253:
7241:
7240:
7238:
7237:
7232:
7226:
7223:
7222:
7215:
7214:
7207:
7200:
7192:
7186:
7185:
7179:
7170:
7164:Data Smoothing
7161:
7154:
7153:External links
7151:
7149:
7148:
7134:
7120:
7108:
7082:
7052:
7027:
7016:(3): 324â342.
6995:
6970:
6945:
6920:
6895:
6888:
6866:
6850:
6837:
6828:
6806:
6784:
6767:
6720:
6703:
6696:
6671:
6643:
6641:
6638:
6637:
6636:
6631:
6629:Moving average
6626:
6621:
6613:
6610:
6609:
6608:
6602:
6596:
6590:
6566:
6560:
6552:
6549:
6548:
6547:
6532:
6525:
6521:
6517:
6514:
6511:
6508:
6505:
6502:
6499:
6496:
6493:
6490:
6487:
6483:
6479:
6474:
6470:
6466:
6463:
6458:
6454:
6450:
6447:
6445:
6441:
6438:
6435:
6431:
6427:
6426:
6421:
6418:
6415:
6411:
6407:
6404:
6401:
6398:
6395:
6392:
6389:
6384:
6381:
6378:
6374:
6370:
6365:
6362:
6359:
6355:
6351:
6346:
6342:
6338:
6335:
6332:
6329:
6327:
6323:
6319:
6315:
6314:
6309:
6306:
6303:
6299:
6295:
6292:
6289:
6286:
6283:
6280:
6277:
6272:
6269:
6266:
6262:
6258:
6253:
6249:
6245:
6242:
6239:
6236:
6234:
6230:
6226:
6222:
6221:
6218:
6213:
6210:
6207:
6203:
6199:
6194:
6191:
6188:
6184:
6180:
6177:
6174:
6171:
6168:
6165:
6162:
6159:
6154:
6151:
6148:
6144:
6140:
6135:
6131:
6127:
6124:
6121:
6118:
6116:
6112:
6108:
6104:
6103:
6098:
6094:
6090:
6087:
6085:
6081:
6077:
6073:
6072:
6040:
6019:
5997:
5993:
5981:
5980:
5969:
5966:
5963:
5960:
5957:
5954:
5951:
5948:
5945:
5934:
5928:
5925:
5922:
5919:
5916:
5913:
5910:
5907:
5903:
5897:
5892:
5889:
5886:
5882:
5875:
5870:
5866:
5851:
5850:
5839:
5836:
5833:
5830:
5827:
5824:
5821:
5818:
5815:
5802:
5798:
5792:
5789:
5786:
5783:
5780:
5777:
5774:
5771:
5767:
5759:
5754:
5751:
5748:
5744:
5738:
5735:
5730:
5725:
5721:
5697:
5677:
5674:
5671:
5668:
5665:
5662:
5659:
5656:
5653:
5631:
5627:
5615:
5614:
5598:
5592:
5586:
5582:
5578:
5573:
5570:
5567:
5563:
5556:
5553:
5550:
5545:
5539:
5535:
5531:
5526:
5523:
5520:
5516:
5509:
5504:
5498:
5494:
5490:
5485:
5482:
5479:
5475:
5467:
5461:
5458:
5453:
5450:
5448:
5444:
5440:
5436:
5435:
5412:
5385:
5382:
5379:
5376:
5373:
5353:
5329:
5326:
5323:
5320:
5317:
5297:
5273:
5270:
5267:
5264:
5261:
5241:
5230:
5229:
5214:
5207:
5203:
5199:
5196:
5193:
5190:
5187:
5184:
5181:
5178:
5175:
5172:
5169:
5165:
5161:
5156:
5152:
5148:
5145:
5140:
5136:
5132:
5129:
5126:
5124:
5120:
5117:
5114:
5110:
5106:
5105:
5100:
5097:
5094:
5090:
5086:
5083:
5080:
5077:
5074:
5071:
5064:
5060:
5054:
5050:
5044:
5041:
5038:
5036:
5032:
5028:
5024:
5023:
5018:
5015:
5012:
5008:
5004:
5001:
4998:
4995:
4992:
4989:
4986:
4981:
4978:
4975:
4971:
4967:
4962:
4958:
4954:
4951:
4948:
4945:
4943:
4939:
4935:
4931:
4930:
4927:
4922:
4919:
4916:
4912:
4908:
4903:
4900:
4897:
4893:
4889:
4886:
4883:
4880:
4877:
4874:
4871:
4864:
4861:
4858:
4854:
4848:
4844:
4838:
4835:
4832:
4830:
4826:
4822:
4818:
4817:
4812:
4808:
4804:
4801:
4799:
4795:
4791:
4787:
4786:
4763:
4743:
4740:
4737:
4734:
4731:
4709:
4706:
4703:
4699:
4676:
4673:
4670:
4666:
4642:
4639:
4619:
4599:
4590:at every time
4577:
4573:
4550:
4546:
4523:
4519:
4498:
4476:
4472:
4448:
4425:
4405:
4402:
4399:
4379:
4374:
4370:
4346:multiplicative
4330:
4327:
4326:
4325:
4310:
4307:
4303:
4299:
4295:
4291:
4287:
4283:
4279:
4275:
4269:
4266:
4263:
4259:
4254:
4251:
4249:
4245:
4241:
4237:
4236:
4232:
4228:
4224:
4220:
4216:
4212:
4208:
4204:
4201:
4198:
4196:
4192:
4188:
4184:
4183:
4162:
4149:
4143:
4142:
4127:
4122:
4118:
4114:
4111:
4106:
4102:
4098:
4095:
4093:
4089:
4086:
4083:
4079:
4075:
4074:
4070:
4066:
4063:
4060:
4056:
4052:
4049:
4046:
4043:
4040:
4037:
4033:
4029:
4025:
4021:
4018:
4015:
4013:
4010:
4006:
4002:
3998:
3997:
3993:
3989:
3986:
3983:
3979:
3975:
3972:
3969:
3966:
3963:
3960:
3955:
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2023:
2003:
1981:
1978:
1975:
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1969:
1962:
1959:
1933:
1929:
1908:
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1899:
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1326:
1323:
1298:
1294:
1290:
1277:is minimized.
1264:
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1207:
1183:
1159:
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869:
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719:
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698:
694:
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628:
624:
599:{\textstyle t}
595:
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569:
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480:
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453:
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389:
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359:
348:
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332:
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200:
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178:{\textstyle x}
174:
154:
149:
145:
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121:
118:
115:
95:
90:
86:
82:
15:
9:
6:
4:
3:
2:
9639:
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9547:
9544:Quantitative
9539:
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9525:
9520:
9519:
9516:
9504:
9503:
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9479:
9474:
9468:
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9456:
9455:
9452:
9438:
9435:
9433:
9432:Geostatistics
9430:
9428:
9425:
9423:
9420:
9418:
9415:
9414:
9412:
9410:
9406:
9400:
9399:Psychometrics
9397:
9395:
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9390:
9387:
9385:
9382:
9380:
9377:
9375:
9372:
9370:
9367:
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9287:
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9282:
9280:
9276:
9273:
9271:
9268:
9267:
9265:
9263:
9262:Biostatistics
9259:
9255:
9251:
9246:
9242:
9224:
9223:Log-rank test
9221:
9220:
9218:
9214:
9208:
9205:
9204:
9202:
9200:
9196:
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9124:
9121:
9120:
9118:
9116:
9112:
9106:
9103:
9101:
9098:
9096:
9094:(BoxâJenkins)
9090:
9088:
9085:
9083:
9080:
9076:
9073:
9072:
9071:
9068:
9067:
9065:
9063:
9059:
9053:
9050:
9048:
9047:DurbinâWatson
9045:
9043:
9037:
9035:
9032:
9030:
9029:DickeyâFuller
9027:
9026:
9024:
9020:
9014:
9011:
9009:
9006:
9004:
9003:Cointegration
9001:
8999:
8996:
8994:
8991:
8989:
8986:
8984:
8981:
8979:
8978:Decomposition
8976:
8975:
8973:
8969:
8966:
8964:
8960:
8950:
8947:
8946:
8945:
8942:
8941:
8940:
8937:
8933:
8930:
8929:
8928:
8925:
8923:
8920:
8918:
8915:
8913:
8910:
8908:
8905:
8903:
8900:
8898:
8895:
8893:
8890:
8889:
8887:
8885:
8881:
8875:
8872:
8870:
8867:
8865:
8862:
8860:
8857:
8855:
8852:
8850:
8849:Cohen's kappa
8847:
8846:
8844:
8842:
8838:
8834:
8830:
8826:
8822:
8818:
8813:
8809:
8795:
8792:
8790:
8787:
8785:
8782:
8780:
8777:
8776:
8774:
8772:
8768:
8762:
8758:
8754:
8748:
8746:
8743:
8742:
8740:
8738:
8734:
8728:
8725:
8723:
8720:
8718:
8715:
8713:
8710:
8708:
8705:
8703:
8702:Nonparametric
8700:
8698:
8695:
8694:
8692:
8688:
8682:
8679:
8677:
8674:
8672:
8669:
8667:
8664:
8663:
8661:
8659:
8655:
8649:
8646:
8644:
8641:
8639:
8636:
8634:
8631:
8629:
8626:
8625:
8623:
8621:
8617:
8611:
8608:
8606:
8603:
8601:
8598:
8596:
8593:
8592:
8590:
8588:
8584:
8580:
8573:
8570:
8568:
8565:
8564:
8560:
8556:
8540:
8537:
8536:
8535:
8532:
8530:
8527:
8525:
8522:
8518:
8515:
8513:
8510:
8509:
8508:
8505:
8504:
8502:
8500:
8496:
8486:
8483:
8479:
8473:
8471:
8465:
8463:
8457:
8456:
8455:
8452:
8451:Nonparametric
8449:
8447:
8441:
8437:
8434:
8433:
8432:
8426:
8422:
8421:Sample median
8419:
8418:
8417:
8414:
8413:
8411:
8409:
8405:
8397:
8394:
8392:
8389:
8387:
8384:
8383:
8382:
8379:
8377:
8374:
8372:
8366:
8364:
8361:
8359:
8356:
8354:
8351:
8349:
8346:
8344:
8342:
8338:
8336:
8333:
8332:
8330:
8328:
8324:
8318:
8316:
8312:
8310:
8308:
8303:
8301:
8296:
8292:
8291:
8288:
8285:
8283:
8279:
8269:
8266:
8264:
8261:
8259:
8256:
8255:
8253:
8251:
8247:
8241:
8238:
8234:
8231:
8230:
8229:
8226:
8222:
8219:
8218:
8217:
8214:
8212:
8209:
8208:
8206:
8204:
8200:
8192:
8189:
8187:
8184:
8183:
8182:
8179:
8177:
8174:
8172:
8169:
8167:
8164:
8162:
8159:
8157:
8154:
8153:
8151:
8149:
8145:
8139:
8136:
8132:
8129:
8125:
8122:
8120:
8117:
8116:
8115:
8112:
8111:
8110:
8107:
8103:
8100:
8098:
8095:
8093:
8090:
8088:
8085:
8084:
8083:
8080:
8079:
8077:
8075:
8071:
8068:
8066:
8062:
8056:
8053:
8051:
8048:
8044:
8041:
8040:
8039:
8036:
8034:
8031:
8027:
8026:loss function
8024:
8023:
8022:
8019:
8015:
8012:
8010:
8007:
8005:
8002:
8001:
8000:
7997:
7995:
7992:
7990:
7987:
7983:
7980:
7978:
7975:
7973:
7967:
7964:
7963:
7962:
7959:
7955:
7952:
7950:
7947:
7945:
7942:
7941:
7940:
7937:
7933:
7930:
7928:
7925:
7924:
7923:
7920:
7916:
7913:
7912:
7911:
7908:
7904:
7901:
7900:
7899:
7896:
7894:
7891:
7889:
7886:
7884:
7881:
7880:
7878:
7876:
7872:
7868:
7864:
7859:
7855:
7841:
7838:
7836:
7833:
7831:
7828:
7826:
7823:
7822:
7820:
7818:
7814:
7808:
7805:
7803:
7800:
7798:
7795:
7794:
7792:
7788:
7782:
7779:
7777:
7774:
7772:
7769:
7767:
7764:
7762:
7759:
7757:
7754:
7752:
7749:
7748:
7746:
7744:
7740:
7734:
7731:
7729:
7728:Questionnaire
7726:
7724:
7721:
7717:
7714:
7712:
7709:
7708:
7707:
7704:
7703:
7701:
7699:
7695:
7689:
7686:
7684:
7681:
7679:
7676:
7674:
7671:
7669:
7666:
7664:
7661:
7659:
7656:
7654:
7651:
7650:
7648:
7646:
7642:
7638:
7634:
7629:
7625:
7611:
7608:
7606:
7603:
7601:
7598:
7596:
7593:
7591:
7588:
7586:
7583:
7581:
7578:
7576:
7573:
7571:
7568:
7566:
7563:
7561:
7558:
7556:
7555:Control chart
7553:
7551:
7548:
7546:
7543:
7541:
7538:
7537:
7535:
7533:
7529:
7523:
7520:
7516:
7513:
7511:
7508:
7507:
7506:
7503:
7501:
7498:
7496:
7493:
7492:
7490:
7488:
7484:
7478:
7475:
7473:
7470:
7468:
7465:
7464:
7462:
7458:
7452:
7449:
7448:
7446:
7444:
7440:
7428:
7425:
7423:
7420:
7418:
7415:
7414:
7413:
7410:
7408:
7405:
7404:
7402:
7400:
7396:
7390:
7387:
7385:
7382:
7380:
7377:
7375:
7372:
7370:
7367:
7365:
7362:
7360:
7357:
7356:
7354:
7352:
7348:
7342:
7339:
7337:
7334:
7330:
7327:
7325:
7322:
7320:
7317:
7315:
7312:
7310:
7307:
7305:
7302:
7300:
7297:
7295:
7292:
7290:
7287:
7285:
7282:
7281:
7280:
7277:
7276:
7274:
7272:
7268:
7265:
7263:
7259:
7255:
7251:
7246:
7242:
7236:
7233:
7231:
7228:
7227:
7224:
7220:
7213:
7208:
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7174:
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7169:
7165:
7162:
7160:
7157:
7156:
7144:
7138:
7130:
7124:
7117:
7112:
7097:. 29 May 2011
7096:
7092:
7086:
7070:
7066:
7062:
7056:
7041:
7037:
7031:
7023:
7019:
7015:
7011:
7010:
7002:
7000:
6981:
6974:
6959:
6955:
6949:
6934:
6930:
6924:
6909:
6905:
6899:
6891:
6889:9781478628248
6885:
6881:
6877:
6870:
6862:
6861:
6854:
6847:
6841:
6832:
6817:
6814:Nau, Robert.
6810:
6794:
6788:
6780:
6779:
6771:
6763:
6759:
6755:
6751:
6750:
6745:
6741:reprinted in
6738:
6734:
6730:
6724:
6716:
6715:
6707:
6699:
6697:0-13-214635-5
6693:
6690:. p. 5.
6689:
6688:Prentice Hall
6685:
6678:
6676:
6659:
6653:
6651:
6649:
6644:
6635:
6632:
6630:
6627:
6625:
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6619:
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6615:
6606:
6603:
6600:
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6512:
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6506:
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6456:
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6409:
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6399:
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6382:
6379:
6376:
6372:
6368:
6363:
6360:
6357:
6353:
6349:
6344:
6340:
6333:
6330:
6328:
6321:
6317:
6307:
6304:
6301:
6297:
6290:
6287:
6284:
6278:
6270:
6267:
6264:
6260:
6256:
6251:
6247:
6240:
6237:
6235:
6228:
6224:
6211:
6208:
6205:
6201:
6197:
6192:
6189:
6186:
6182:
6172:
6169:
6166:
6160:
6152:
6149:
6146:
6142:
6138:
6133:
6129:
6122:
6119:
6117:
6110:
6106:
6096:
6092:
6088:
6086:
6079:
6075:
6063:
6062:
6061:
6058:
6038:
6017:
5995:
5991:
5967:
5964:
5961:
5958:
5955:
5952:
5949:
5946:
5943:
5932:
5926:
5923:
5917:
5914:
5911:
5905:
5901:
5895:
5890:
5887:
5884:
5880:
5873:
5868:
5864:
5856:
5855:
5854:
5837:
5834:
5831:
5828:
5825:
5822:
5819:
5816:
5813:
5800:
5796:
5790:
5787:
5781:
5778:
5775:
5769:
5765:
5757:
5752:
5749:
5746:
5742:
5736:
5733:
5728:
5723:
5719:
5711:
5710:
5709:
5695:
5675:
5672:
5669:
5666:
5663:
5660:
5657:
5654:
5651:
5629:
5625:
5596:
5590:
5584:
5580:
5576:
5571:
5568:
5565:
5561:
5554:
5551:
5548:
5543:
5537:
5533:
5529:
5524:
5521:
5518:
5514:
5507:
5502:
5496:
5492:
5488:
5483:
5480:
5477:
5473:
5465:
5459:
5456:
5451:
5449:
5442:
5438:
5426:
5425:
5424:
5410:
5401:
5399:
5383:
5380:
5377:
5374:
5371:
5351:
5343:
5327:
5324:
5321:
5318:
5315:
5295:
5287:
5271:
5268:
5265:
5262:
5259:
5239:
5212:
5205:
5194:
5191:
5188:
5182:
5179:
5176:
5173:
5170:
5167:
5163:
5154:
5150:
5146:
5143:
5138:
5134:
5127:
5125:
5118:
5115:
5112:
5108:
5098:
5095:
5092:
5088:
5081:
5078:
5075:
5069:
5062:
5058:
5052:
5048:
5042:
5039:
5037:
5030:
5026:
5016:
5013:
5010:
5006:
4999:
4996:
4993:
4987:
4979:
4976:
4973:
4969:
4965:
4960:
4956:
4949:
4946:
4944:
4937:
4933:
4920:
4917:
4914:
4910:
4906:
4901:
4898:
4895:
4891:
4881:
4878:
4875:
4869:
4862:
4859:
4856:
4852:
4846:
4842:
4836:
4833:
4831:
4824:
4820:
4810:
4806:
4802:
4800:
4793:
4789:
4777:
4776:
4775:
4761:
4741:
4738:
4735:
4732:
4729:
4707:
4704:
4701:
4697:
4674:
4671:
4668:
4664:
4654:
4640:
4637:
4617:
4597:
4575:
4571:
4548:
4544:
4521:
4517:
4496:
4474:
4470:
4460:
4446:
4437:
4423:
4403:
4400:
4397:
4377:
4372:
4368:
4359:
4358:rule of thumb
4355:
4349:
4347:
4343:
4338:
4336:
4308:
4301:
4297:
4293:
4289:
4285:
4281:
4277:
4267:
4264:
4261:
4257:
4252:
4250:
4243:
4239:
4230:
4226:
4222:
4218:
4214:
4210:
4206:
4202:
4199:
4197:
4190:
4186:
4174:
4173:
4172:
4170:
4165:
4161:
4157:
4152:
4148:
4125:
4120:
4116:
4112:
4109:
4104:
4100:
4096:
4094:
4087:
4084:
4081:
4077:
4068:
4064:
4061:
4058:
4054:
4047:
4044:
4041:
4035:
4031:
4027:
4023:
4019:
4016:
4014:
4008:
4004:
4000:
3991:
3987:
3984:
3981:
3977:
3970:
3967:
3964:
3958:
3953:
3949:
3945:
3942:
3940:
3934:
3930:
3926:
3916:
3912:
3908:
3906:
3900:
3896:
3892:
3882:
3878:
3874:
3872:
3866:
3862:
3858:
3846:
3845:
3844:
3841:
3836:
3829:
3822:
3815:
3810:
3796:
3774:
3768:
3764:
3760:
3755:
3751:
3727:
3702:
3698:
3694:
3691:
3688:
3683:
3679:
3675:
3670:
3667:
3664:
3660:
3652:
3651:
3650:
3634:
3630:
3620:
3618:
3602:
3599:
3596:
3593:
3590:
3570:
3562:
3546:
3543:
3540:
3537:
3534:
3514:
3485:
3482:
3479:
3475:
3468:
3465:
3462:
3456:
3448:
3445:
3442:
3438:
3434:
3429:
3425:
3418:
3415:
3413:
3406:
3402:
3389:
3386:
3383:
3379:
3375:
3370:
3367:
3364:
3360:
3350:
3347:
3344:
3338:
3333:
3329:
3325:
3322:
3320:
3313:
3309:
3297:
3296:
3295:
3281:
3278:
3275:
3246:
3242:
3238:
3233:
3229:
3225:
3223:
3216:
3212:
3202:
3198:
3194:
3192:
3185:
3181:
3169:
3168:
3167:
3153:
3133:
3130:
3127:
3105:
3102:
3099:
3095:
3072:
3069:
3066:
3062:
3041:
3019:
3015:
2994:
2972:
2968:
2947:
2944:
2941:
2919:
2915:
2905:
2902:
2899:
2889:
2887:
2883:
2879:
2875:
2870:
2868:
2864:
2860:
2856:
2852:
2848:
2837:
2835:
2831:
2827:
2808:
2805:
2800:
2792:
2789:
2786:
2780:
2777:
2774:
2769:
2761:
2758:
2755:
2749:
2743:
2740:
2737:
2731:
2728:
2721:
2720:
2719:
2705:
2702:
2697:
2694:
2691:
2687:
2683:
2680:
2677:
2672:
2669:
2666:
2662:
2639:
2635:
2607:
2602:
2598:
2592:
2584:
2581:
2578:
2572:
2568:
2562:
2558:
2552:
2549:
2546:
2538:
2535:
2532:
2526:
2523:
2520:
2515:
2512:
2509:
2505:
2499:
2491:
2488:
2485:
2479:
2474:
2471:
2468:
2464:
2458:
2450:
2447:
2444:
2438:
2433:
2430:
2427:
2423:
2416:
2413:
2410:
2404:
2399:
2395:
2390:
2386:
2383:
2381:
2371:
2368:
2365:
2361:
2355:
2347:
2344:
2341:
2335:
2330:
2327:
2324:
2320:
2313:
2310:
2307:
2301:
2298:
2293:
2289:
2285:
2282:
2280:
2270:
2267:
2264:
2260:
2253:
2250:
2247:
2241:
2236:
2232:
2228:
2225:
2223:
2216:
2212:
2200:
2199:
2198:
2195:
2187:
2185:
2164:
2159:
2155:
2149:
2144:
2141:
2138:
2134:
2130:
2125:
2115:
2112:
2109:
2106:
2103:
2093:
2086:
2081:
2077:
2068:
2063:
2060:
2057:
2053:
2049:
2037:
2036:
2035:
2021:
2001:
1979:
1976:
1973:
1970:
1967:
1957:
1931:
1927:
1906:
1903:
1900:
1897:
1894:
1891:
1888:
1866:
1863:
1860:
1857:
1854:
1844:
1837:
1832:
1828:
1824:
1819:
1815:
1806:
1801:
1797:
1795:
1785:
1769:
1765:
1744:
1722:
1719:
1716:
1712:
1689:
1685:
1662:
1658:
1649:
1646:Note that in
1623:
1619:
1610:
1607:
1600:
1599:
1598:
1596:
1580:
1577:
1574:
1551:
1519:
1516:
1513:
1507:
1504:
1499:
1490:
1487:
1484:
1462:
1458:
1454:
1448:
1444:
1440:
1437:
1434:
1431:
1424:
1423:
1422:
1408:
1388:
1364:
1361:
1358:
1354:
1350:
1347:
1344:
1336:
1332:
1331:time constant
1325:Time constant
1322:
1320:
1316:
1311:
1296:
1292:
1288:
1278:
1262:
1252:
1249:
1246:
1242:
1238:
1233:
1229:
1205:
1197:
1181:
1174:the value of
1173:
1157:
1148:
1134:
1131:
1128:
1106:
1102:
1081:
1061:
1041:
1021:
1001:
981:
973:
955:
952:
949:
945:
922:
918:
895:
891:
870:
867:
864:
861:
858:
850:
834:
811:
803:
800:
797:
793:
789:
784:
780:
773:
770:
765:
762:
759:
755:
751:
746:
743:
740:
736:
729:
726:
723:
717:
712:
708:
704:
701:
696:
692:
684:
683:
682:
679:
677:
673:
668:
664:
660:
656:
652:
642:
626:
622:
613:
609:
593:
573:
570:
567:
558:
542:
538:
529:
508:
504:
478:
474:
451:
447:
424:
421:
418:
414:
393:
390:
387:
384:
381:
373:
357:
330:
327:
324:
320:
315:
312:
309:
305:
298:
295:
292:
286:
281:
277:
273:
270:
268:
261:
257:
247:
243:
239:
237:
230:
226:
214:
213:
212:
198:
195:
192:
172:
147:
143:
119:
116:
113:
88:
84:
71:
69:
65:
61:
57:
53:
49:
44:
41:
37:
33:
29:
28:rule of thumb
25:
21:
9563:
9500:
9488:
9469:
9462:
9374:Econometrics
9324: /
9307:Chemometrics
9284:Epidemiology
9277: /
9250:Applications
9092:ARIMA model
9039:Q-statistic
8997:
8988:Stationarity
8884:Multivariate
8827: /
8823: /
8821:Multivariate
8819: /
8759: /
8755: /
8529:Bayes factor
8428:Signed rank
8340:
8314:
8306:
8294:
7989:Completeness
7825:Cohort study
7723:Opinion poll
7658:Missing data
7645:Study design
7600:Scatter plot
7522:Scatter plot
7515:Spearman's Ï
7477:Grouped data
7137:
7123:
7111:
7099:. Retrieved
7094:
7085:
7073:. Retrieved
7069:the original
7065:inside-r.org
7064:
7055:
7043:. Retrieved
7040:stat.ethz.ch
7039:
7030:
7013:
7007:
6986:. Retrieved
6973:
6963:25 September
6961:. Retrieved
6957:
6948:
6938:25 September
6936:. Retrieved
6933:itl.nist.gov
6932:
6923:
6911:. Retrieved
6898:
6875:
6869:
6859:
6853:
6845:
6840:
6831:
6819:. Retrieved
6809:
6797:. Retrieved
6787:
6777:
6770:
6753:
6747:
6736:
6732:
6723:
6713:
6706:
6683:
6662:. Retrieved
6582:
6578:
6574:
6059:
5982:
5852:
5616:
5402:
5397:
5341:
5285:
5231:
4655:
4461:
4438:
4350:
4345:
4341:
4339:
4332:
4168:
4163:
4159:
4155:
4150:
4146:
4144:
3842:
3834:
3827:
3820:
3813:
3811:
3719:
3621:
3616:
3560:
3506:
3267:
2906:
2903:
2895:
2871:
2866:
2862:
2858:
2854:
2850:
2846:
2843:
2823:
2626:
2196:
2193:
2184:optimization
2181:
1802:
1798:
1793:
1791:
1788:Optimization
1647:
1645:
1540:
1328:
1312:
1279:
1171:
1149:
971:
848:
826:
680:
648:
606:, while the
559:
371:
349:
72:
54:, acting as
45:
23:
19:
18:
9627:Time series
9546:forecasting
9502:WikiProject
9417:Cartography
9379:Jurimetrics
9331:Reliability
9062:Time domain
9041:(LjungâBox)
8963:Time-series
8841:Categorical
8825:Time-series
8817:Categorical
8752:(Bernoulli)
8587:Correlation
8567:Correlation
8363:JarqueâBera
8335:Chi-squared
8097:M-estimator
8050:Asymptotics
7994:Sufficiency
7761:Interaction
7673:Replication
7653:Effect size
7610:Violin plot
7590:Radar chart
7570:Forest plot
7560:Correlogram
7510:Kendall's Ï
6756:(1): 5â10.
6599:LibreOffice
4335:time series
974:applied to
32:time series
9369:Demography
9087:ARMA model
8892:Regression
8469:(Friedman)
8430:(Wilcoxon)
8368:Normality
8358:Lilliefors
8305:Student's
8181:Resampling
8055:Robustness
8043:divergence
8033:Efficiency
7971:(monotone)
7966:Likelihood
7883:Population
7716:Stratified
7668:Population
7487:Dependence
7443:Count data
7374:Percentile
7351:Dispersion
7284:Arithmetic
7219:Statistics
6913:23 January
6589:statistic.
5983:Note that
3812:Note that
2834:Statistics
8750:Logistic
8517:posterior
8443:Rank sum
8191:Jackknife
8186:Bootstrap
8004:Bootstrap
7939:Parameter
7888:Statistic
7683:Statistic
7595:Run chart
7580:Pie chart
7575:Histogram
7565:Fan chart
7540:Bar chart
7422:L-moments
7309:Geometric
7095:Hyndsight
6510:−
6489:−
6417:−
6403:γ
6400:−
6380:−
6369:−
6361:−
6350:−
6334:γ
6305:−
6291:β
6288:−
6268:−
6257:−
6241:β
6209:−
6190:−
6173:α
6170:−
6150:−
6139:−
6123:α
5962:…
5940:for
5915:−
5881:∑
5832:…
5810:for
5779:−
5743:∑
5670:…
5577:−
5552:⋯
5530:−
5489:−
5396:) is the
5381:≤
5378:γ
5375:≤
5352:γ
5340:) is the
5325:≤
5322:β
5319:≤
5296:β
5284:) is the
5269:≤
5266:α
5263:≤
5240:α
5192:−
5171:−
5096:−
5082:γ
5079:−
5043:γ
5014:−
5000:β
4997:−
4977:−
4966:−
4950:β
4918:−
4899:−
4882:α
4879:−
4860:−
4837:α
4290:−
4268:α
4265:−
4258:α
4219:−
4062:−
4048:α
4045:−
4020:α
3985:−
3971:α
3968:−
3946:α
3789:for some
3761:−
3695:⋅
3615:) is the
3600:≤
3597:β
3594:≤
3571:β
3559:) is the
3544:≤
3541:α
3538:≤
3515:α
3483:−
3469:β
3466:−
3446:−
3435:−
3419:β
3387:−
3368:−
3351:α
3348:−
3326:α
3239:−
2960:. We use
2809:…
2793:α
2790:−
2778:…
2762:α
2759:−
2744:α
2741:−
2706:…
2695:−
2681:…
2670:−
2585:α
2582:−
2550:−
2539:α
2536:−
2524:⋯
2513:−
2492:α
2489:−
2472:−
2451:α
2448:−
2431:−
2417:α
2414:−
2387:α
2369:−
2348:α
2345:−
2328:−
2314:α
2311:−
2302:α
2286:α
2268:−
2254:α
2251:−
2229:α
2135:∑
2113:−
2107:∣
2097:^
2087:−
2054:∑
1977:−
1971:∣
1961:^
1901:…
1864:−
1858:∣
1848:^
1838:−
1745:α
1720:−
1624:τ
1617:Δ
1611:≈
1608:α
1581:τ
1578:≪
1572:Δ
1549:Δ
1520:α
1517:−
1508:
1497:Δ
1491:−
1485:τ
1463:τ
1452:Δ
1449:−
1441:−
1432:α
1409:α
1389:τ
1369:%
1362:≈
1348:−
1337:to reach
1297:α
1239:−
1206:α
1182:α
1158:α
1082:α
1062:α
1042:α
1022:α
1002:α
982:α
953:−
868:≤
865:α
862:≤
835:α
801:−
790:−
774:α
763:−
744:−
730:α
727:−
705:α
678:filters.
422:−
388:α
358:α
313:−
299:α
296:−
274:α
9621:Category
9464:Category
9157:Survival
9034:Johansen
8757:Binomial
8712:Isotonic
8299:(normal)
7944:location
7751:Blocking
7706:Sampling
7585:QâQ plot
7550:Box plot
7532:Graphics
7427:Skewness
7417:Kurtosis
7389:Variance
7319:Heronian
7314:Harmonic
7116:tssmooth
6958:duke.edu
6612:See also
4722:at time
4342:additive
4302:″
4286:′
4231:″
4215:′
4069:″
4032:′
4009:″
3992:′
3935:′
3901:″
3867:′
3268:And for
3120:at time
1477:, thus
1172:optimize
9548:methods
9490:Commons
9437:Kriging
9322:Process
9279:studies
9138:Wavelet
8971:General
8138:Plug-in
7932:L space
7711:Cluster
7412:Moments
7230:Outline
6988:23 June
6821:26 July
6030:in the
2872:In the
847:is the
651:Poisson
526:, then
370:is the
64:Poisson
9359:Census
8949:Normal
8897:Manova
8717:Robust
8467:2-way
8459:1-way
8297:-test
7968:
7545:Biplot
7336:Median
7329:Lehmer
7271:Center
7101:5 June
7075:5 June
7045:5 June
6908:SAP AG
6886:
6799:5 July
6795:. NIST
6694:
6664:23 May
6660:. NIST
6620:(ARMA)
6581:, and
6563:Python
5853:where
5344:, and
5232:where
4145:where
3563:, and
3507:where
3007:, and
2836:lore.
1541:where
851:, and
827:where
374:, and
350:where
8983:Trend
8512:prior
8454:anova
8343:-test
8317:-test
8309:-test
8216:Power
8161:Pivot
7954:shape
7949:scale
7399:Shape
7379:Range
7324:Heinz
7299:Cubic
7235:Index
6983:(PDF)
6640:Notes
6593:Stata
4171:are:
2898:trend
2849:= 2/(
406:. If
60:noise
26:is a
9216:Test
8416:Sign
8268:Wald
7341:Mode
7279:Mean
7103:2016
7077:2016
7047:2016
6990:2014
6965:2011
6940:2011
6915:2013
6884:ISBN
6823:2010
6801:2017
6692:ISBN
6666:2010
6607:2016
6570:SPSS
6568:IBM
5644:for
5423:is:
4739:>
4610:mod
4462:Let
4158:and
3279:>
3131:>
1946:and
1881:for
1365:63.2
1329:The
610:and
391:<
385:<
328:>
8396:BIC
8391:AIC
7018:doi
6758:doi
6601:5.2
6520:mod
5202:mod
3294:by
2046:SSE
22:or
9623::
7093:.
7063:.
7038:.
7012:.
6998:^
6956:.
6931:.
6906:.
6882:.
6880:53
6754:20
6752:.
6737:52
6735:.
6686:.
6674:^
6647:^
6577:,
6043:th
5400:.
5288:,
4509:,
4459:.
4436:.
3809:.
3619:.
2824:A
1784:.
1650:,
1597:,
1505:ln
1147:.
9537:e
9530:t
9523:v
8341:G
8315:F
8307:t
8295:Z
8014:V
8009:U
7211:e
7204:t
7197:v
7145:.
7131:.
7105:.
7079:.
7049:.
7024:.
7020::
7014:6
6992:.
6967:.
6942:.
6917:.
6892:.
6863:.
6825:.
6803:.
6764:.
6760::
6739:.
6700:.
6668:.
6583:q
6579:d
6575:p
6557:R
6531:,
6524:L
6516:)
6513:1
6507:m
6504:(
6501:+
6498:1
6495:+
6492:L
6486:t
6482:c
6478:+
6473:t
6469:b
6465:m
6462:+
6457:t
6453:s
6449:=
6440:m
6437:+
6434:t
6430:F
6420:L
6414:t
6410:c
6406:)
6397:1
6394:(
6391:+
6388:)
6383:1
6377:t
6373:b
6364:1
6358:t
6354:s
6345:t
6341:x
6337:(
6331:=
6322:t
6318:c
6308:1
6302:t
6298:b
6294:)
6285:1
6282:(
6279:+
6276:)
6271:1
6265:t
6261:s
6252:t
6248:s
6244:(
6238:=
6229:t
6225:b
6217:)
6212:1
6206:t
6202:b
6198:+
6193:1
6187:t
6183:s
6179:(
6176:)
6167:1
6164:(
6161:+
6158:)
6153:L
6147:t
6143:c
6134:t
6130:x
6126:(
6120:=
6111:t
6107:s
6097:0
6093:x
6089:=
6080:0
6076:s
6039:j
6018:x
5996:j
5992:A
5968:N
5965:,
5959:,
5956:2
5953:,
5950:1
5947:=
5944:j
5933:L
5927:i
5924:+
5921:)
5918:1
5912:j
5909:(
5906:L
5902:x
5896:L
5891:1
5888:=
5885:i
5874:=
5869:j
5865:A
5838:L
5835:,
5829:,
5826:2
5823:,
5820:1
5817:=
5814:i
5801:j
5797:A
5791:i
5788:+
5785:)
5782:1
5776:j
5773:(
5770:L
5766:x
5758:N
5753:1
5750:=
5747:j
5737:N
5734:1
5729:=
5724:i
5720:c
5696:N
5676:L
5673:,
5667:,
5664:2
5661:,
5658:1
5655:=
5652:i
5630:i
5626:c
5597:)
5591:L
5585:L
5581:x
5572:L
5569:+
5566:L
5562:x
5555:+
5549:+
5544:L
5538:2
5534:x
5525:2
5522:+
5519:L
5515:x
5508:+
5503:L
5497:1
5493:x
5484:1
5481:+
5478:L
5474:x
5466:(
5460:L
5457:1
5452:=
5443:0
5439:b
5411:b
5384:1
5372:0
5364:(
5328:1
5316:0
5308:(
5272:1
5260:0
5252:(
5213:,
5206:L
5198:)
5195:1
5189:m
5186:(
5183:+
5180:1
5177:+
5174:L
5168:t
5164:c
5160:)
5155:t
5151:b
5147:m
5144:+
5139:t
5135:s
5131:(
5128:=
5119:m
5116:+
5113:t
5109:F
5099:L
5093:t
5089:c
5085:)
5076:1
5073:(
5070:+
5063:t
5059:s
5053:t
5049:x
5040:=
5031:t
5027:c
5017:1
5011:t
5007:b
5003:)
4994:1
4991:(
4988:+
4985:)
4980:1
4974:t
4970:s
4961:t
4957:s
4953:(
4947:=
4938:t
4934:b
4926:)
4921:1
4915:t
4911:b
4907:+
4902:1
4896:t
4892:s
4888:(
4885:)
4876:1
4873:(
4870:+
4863:L
4857:t
4853:c
4847:t
4843:x
4834:=
4825:t
4821:s
4811:0
4807:x
4803:=
4794:0
4790:s
4762:t
4742:0
4736:m
4733:+
4730:t
4708:m
4705:+
4702:t
4698:x
4675:m
4672:+
4669:t
4665:F
4641:L
4638:2
4618:L
4598:t
4576:t
4572:c
4549:t
4545:c
4522:t
4518:b
4497:t
4475:t
4471:s
4447:L
4424:L
4404:0
4401:=
4398:t
4378:,
4373:t
4369:x
4309:.
4306:)
4298:t
4294:s
4282:t
4278:s
4274:(
4262:1
4253:=
4244:t
4240:b
4227:t
4223:s
4211:t
4207:s
4203:2
4200:=
4191:t
4187:a
4169:t
4164:t
4160:b
4156:t
4151:t
4147:a
4126:,
4121:t
4117:b
4113:m
4110:+
4105:t
4101:a
4097:=
4088:m
4085:+
4082:t
4078:F
4065:1
4059:t
4055:s
4051:)
4042:1
4039:(
4036:+
4028:t
4024:s
4017:=
4005:t
4001:s
3988:1
3982:t
3978:s
3974:)
3965:1
3962:(
3959:+
3954:t
3950:x
3943:=
3931:t
3927:s
3917:0
3913:x
3909:=
3897:0
3893:s
3883:0
3879:x
3875:=
3863:0
3859:s
3838:0
3835:b
3833:+
3831:0
3828:s
3826:=
3824:1
3821:F
3817:0
3814:F
3797:n
3775:n
3769:0
3765:x
3756:n
3752:x
3728:b
3703:t
3699:b
3692:m
3689:+
3684:t
3680:s
3676:=
3671:m
3668:+
3665:t
3661:F
3635:t
3631:x
3603:1
3591:0
3583:(
3547:1
3535:0
3527:(
3486:1
3480:t
3476:b
3472:)
3463:1
3460:(
3457:+
3454:)
3449:1
3443:t
3439:s
3430:t
3426:s
3422:(
3416:=
3407:t
3403:b
3395:)
3390:1
3384:t
3380:b
3376:+
3371:1
3365:t
3361:s
3357:(
3354:)
3345:1
3342:(
3339:+
3334:t
3330:x
3323:=
3314:t
3310:s
3282:0
3276:t
3247:0
3243:x
3234:1
3230:x
3226:=
3217:0
3213:b
3203:0
3199:x
3195:=
3186:0
3182:s
3154:t
3134:0
3128:m
3106:m
3103:+
3100:t
3096:x
3073:m
3070:+
3067:t
3063:F
3042:t
3020:t
3016:b
2995:t
2973:t
2969:s
2948:0
2945:=
2942:t
2920:t
2916:x
2867:k
2863:k
2859:k
2855:k
2851:k
2847:α
2806:,
2801:n
2797:)
2787:1
2784:(
2781:,
2775:,
2770:2
2766:)
2756:1
2753:(
2750:,
2747:)
2738:1
2735:(
2732:,
2729:1
2703:,
2698:n
2692:t
2688:s
2684:,
2678:,
2673:1
2667:t
2663:s
2640:t
2636:s
2608:.
2603:0
2599:x
2593:t
2589:)
2579:1
2576:(
2573:+
2569:]
2563:1
2559:x
2553:1
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2543:)
2533:1
2530:(
2527:+
2521:+
2516:3
2510:t
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2500:3
2496:)
2486:1
2483:(
2480:+
2475:2
2469:t
2465:x
2459:2
2455:)
2445:1
2442:(
2439:+
2434:1
2428:t
2424:x
2420:)
2411:1
2408:(
2405:+
2400:t
2396:x
2391:[
2384:=
2372:2
2366:t
2362:s
2356:2
2352:)
2342:1
2339:(
2336:+
2331:1
2325:t
2321:x
2317:)
2308:1
2305:(
2299:+
2294:t
2290:x
2283:=
2271:1
2265:t
2261:s
2257:)
2248:1
2245:(
2242:+
2237:t
2233:x
2226:=
2217:t
2213:s
2165:2
2160:t
2156:e
2150:T
2145:1
2142:=
2139:t
2131:=
2126:2
2122:)
2116:1
2110:t
2104:t
2094:y
2082:t
2078:y
2074:(
2069:T
2064:1
2061:=
2058:t
2050:=
2022:t
2002:t
1980:1
1974:t
1968:t
1958:y
1932:t
1928:y
1907:T
1904:,
1898:,
1895:1
1892:=
1889:t
1867:1
1861:t
1855:t
1845:y
1833:t
1829:y
1825:=
1820:t
1816:e
1794:α
1770:0
1766:s
1723:1
1717:t
1713:s
1690:0
1686:x
1663:0
1659:s
1620:T
1575:T
1552:T
1523:)
1514:1
1511:(
1500:T
1488:=
1459:/
1455:T
1445:e
1438:1
1435:=
1359:e
1355:/
1351:1
1345:1
1293:/
1289:3
1263:2
1259:)
1253:1
1250:+
1247:t
1243:x
1234:t
1230:s
1226:(
1135:0
1132:=
1129:t
1107:0
1103:x
956:1
950:t
946:s
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896:t
892:s
871:1
859:0
812:.
809:)
804:1
798:t
794:s
785:t
781:x
777:(
771:+
766:1
760:t
756:s
752:=
747:1
741:t
737:s
733:)
724:1
721:(
718:+
713:t
709:x
702:=
697:t
693:s
627:t
623:b
594:t
574:m
571:+
568:t
543:t
539:x
514:}
509:t
505:x
501:{
479:t
475:s
452:t
448:s
425:1
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415:s
394:1
382:0
331:0
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321:,
316:1
310:t
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302:)
293:1
290:(
287:+
282:t
278:x
271:=
262:t
258:s
248:0
244:x
240:=
231:0
227:s
199:0
196:=
193:t
173:x
153:}
148:t
144:s
140:{
120:0
117:=
114:t
94:}
89:t
85:x
81:{
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