1117:(1990) show that residual-based unit root tests applied to the estimated cointegrating residuals do not have the usual DickeyâFuller distributions under the null hypothesis of no-cointegration. Because of the spurious regression phenomenon under the null hypothesis, the distribution of these tests have asymptotic distributions that depend on (1) the number of deterministic trend terms and (2) the number of variables with which co-integration is being tested. These distributions are known as PhillipsâOuliaris distributions and critical values have been tabulated. In finite samples, a superior alternative to the use of these asymptotic critical value is to generate critical values from simulations.
4071:
4057:
4095:
4083:
1171:
economic crises, changes in the people's preferences and behaviour accordingly, policy or regime alteration, and organizational or institutional developments. This is especially likely to be the case if the sample period is long. To take this issue into account, tests have been introduced for cointegration with one unknown
1170:
Tests for cointegration assume that the cointegrating vector is constant during the period of study. In reality, it is possible that the long-run relationship between the underlying variables change (shifts in the cointegrating vector can occur). The reason for this might be technological progress,
1101:
is a test for cointegration that allows for more than one cointegrating relationship, unlike the EngleâGranger method, but this test is subject to asymptotic properties, i.e. large samples. If the sample size is too small then the results will not be reliable and one should use Auto
Regressive
288:
trends can be co-integrated only if there is a genuine relationship between the two. Thus the standard current methodology for time series regressions is to check all-time series involved for integration. If there are
971:
1088:
255:
processes, Granger and
Newbold showed that de-trending does not work to eliminate the problem of spurious correlation, and that the superior alternative is to check for co-integration. Two series with
569:
887:
1158:
series, but it is more generally applicable and can be used for variables integrated of higher order (to detect correlated accelerations or other second-difference effects).
845:
815:
336:
For example, regressing the consumption series for any country (e.g. Fiji) against the GNP for a randomly selected dissimilar country (e.g. Afghanistan) might give a high
1026:
325:
The possible presence of cointegration must be taken into account when choosing a technique to test hypotheses concerning the relationship between two variables having
782:
677:
622:
482:
1000:
762:
735:
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649:
599:
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455:
428:
1154:
377:
318:
284:
251:
179:
3192:
1640:
Koop, G.; Strachan, R.; van Dijk, H.K.; Villani, M. (January 1, 2006). "Chapter 17: Bayesian
Approaches to Cointegration". In Mills, T.C.; Patterson, K. (eds.).
3697:
122:
are cointegrated. Cointegration has become an important property in contemporary time series analysis. Time series often have trendsâeither deterministic or
329:(i.e. integrated of at least order one). The usual procedure for testing hypotheses concerning the relationship between non-stationary variables was to run
3847:
3471:
2112:
3245:
1256:
3684:
1187:
have been proposed to compute the posterior distribution of the number of cointegrating relationships and the cointegrating linear combinations.
892:
1745:
1721:
1691:
1651:
2107:
1807:
1254:
Yule, U. (1926). "Why do we sometimes get nonsense-correlations between time series? - A study in sampling and the nature of time series".
1756:
2711:
1859:
130:(1982) provided statistical evidence that many US macroeconomic time series (like GNP, wages, employment, etc.) have stochastic trends.
4099:
784:
is estimated, the critical values of this ADF test are non-standard, and increase in absolute value as more regressors are included.
3494:
3386:
652:
3672:
3546:
1031:
3730:
3391:
3136:
2507:
2097:
2721:
333:(OLS) regressions on data which had been differenced. This method is biased if the non-stationary variables are cointegrated.
3781:
2993:
2800:
2689:
2647:
1886:
150:, then the series are said to be cointegrated. A common example is where the individual series are first-order integrated (
4121:
4024:
2983:
1227:
3033:
3575:
3524:
3509:
3499:
3368:
3240:
3207:
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2818:
1206:
1162:
extends the cointegration technique beyond two variables, and occasionally to variables integrated at different orders.
3644:
2945:
3919:
3720:
2699:
2368:
1832:
68:
of this collection is integrated of order less than d, then the collection is said to be co-integrated. Formally, if (
3804:
3771:
322:
series on both sides of the regression relationship, then it is possible for regressions to give misleading results.
3776:
3519:
3278:
3184:
3164:
3072:
2783:
2601:
2084:
1956:
215:, since standard detrending techniques can result in data that are still non-stationary. Granger's 1987 paper with
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2716:
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3025:
2879:
2808:
2728:
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2567:
2275:
1996:
1764:
1484:
Pesaran, M.H.; Shin, Y.; Smith, R.J. (2001). "Bounds testing approaches to the analysis of level relationships".
1450:
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4019:
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2490:
2399:
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1961:
1800:
1463:
1378:
Granger, Clive (1981). "Some
Properties of Time Series Data and Their Use in Econometric Model Specification".
787:
If the variables are found to be cointegrated, a second-stage regression is conducted. This is a regression of
517:
3056:
3040:
3928:
3541:
3481:
3418:
2778:
2640:
2630:
2480:
2394:
1601:"Tests for cointegration with two unknown regime shifts with an application to financial market integration"
1380:
1304:
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2265:
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1948:
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1313:
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2004:
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2129:
2009:
1110:
975:
If the variables are not cointegrated (if we cannot reject the null of no cointegration when testing
458:
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147:
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58:
1318:
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820:
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1981:
1976:
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1281:
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184:
143:
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1683:
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464:=1 and are cointegrated, then a linear combination of them must be stationary for some value of
1713:
1600:
1005:
381:
series which are not directly causally related may nonetheless show a significant correlation.
3981:
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1938:
1741:
1735:
1717:
1687:
1647:
1201:
200:
1341:
Mahdavi
Damghani, Babak; et al. (2012). "The Misleading Value of Measured Correlation".
4006:
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2551:
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2500:
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1881:
1225:
Nelson, C.R; Plosser, C.I (1982). "Trends and random walks in macroeconomic time series".
1130:
353:
294:
260:
227:
155:
127:
340:
relationship (suggesting high explanatory power on Fiji's consumption from
Afghanistan's
3872:
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2330:
2260:
1906:
1672:
195:
The first to introduce and analyse the concept of spuriousâor nonsenseâregression was
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3202:
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2611:
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1926:
54:
23:
1408:
2860:
2340:
2040:
1971:
1921:
1896:
1816:
1618:
1451:
https://www.econ.queensu.ca/sites/econ.queensu.ca/files/wpaper/qed_wp_1227.pdf
123:
1409:"Co-integration and error correction: Representation, estimation and testing"
3013:
2865:
2485:
2280:
2192:
2177:
2172:
2137:
1757:"A Drunk and her Dog: An Illustration of Cointegration and Error Correction"
337:
326:
196:
1641:
1175:, and tests for cointegration with two unknown breaks are also available.
966:{\displaystyle \Delta y_{t}=\Delta x_{t}b+\alpha u_{t-1}+\varepsilon _{t}}
2529:
2147:
2024:
2019:
2014:
1986:
1302:
Granger, C.; Newbold, P. (1974). "Spurious
Regressions in Econometrics".
4034:
3735:
1551:
1506:
1437:
1356:
1277:
679:
is unknown, we must first estimate it. This is typically done by using
3956:
2937:
2911:
2891:
2142:
1933:
1567:"Residual-based tests for cointegration in models with regime shifts"
1543:
1497:
1429:
1269:
219:
formalized the cointegrating vector approach, and coined the term.
183:) but some (cointegrating) vector of coefficients exists to form a
1523:"Asymptotic Properties of Residual Based Tests for Cointegration"
1876:
3845:
3412:
3159:
2458:
2228:
1845:
1789:
399:
Error correction model § Engle and
Granger 2-step approach
341:
1785:
1083:{\displaystyle \Delta y_{t}=\Delta x_{t}b+\varepsilon _{t}}
57:
variables. First, all of the series must be integrated of
203:
on non-stationary time series data, which Nobel laureate
389:
The six main methods for testing for cointegration are:
16:
Statistical property of collections of time series data
1133:
1034:
1008:
981:
895:
853:
823:
793:
770:
743:
716:
689:
665:
630:
610:
580:
520:
490:
470:
436:
409:
356:
297:
263:
230:
211:
showed to be a dangerous approach that could produce
158:
3698:
Autoregressive conditional heteroskedasticity (ARCH)
4005:
3942:
3895:
3858:
3813:
3795:
3762:
3753:
3711:
3658:
3619:
3568:
3559:
3480:
3437:
3367:
3333:
3287:
3254:
3216:
3183:
3095:
3004:
2923:
2878:
2846:
2799:
2744:
2670:
2661:
2471:
2413:
2387:
2339:
2294:
2241:
2128:
2083:
2057:
2039:
1995:
1947:
1867:
1858:
737:and an intercept). Then, we can run an ADF test on
1671:
1148:
1082:
1020:
994:
965:
881:
839:
809:
776:
756:
729:
702:
671:
643:
616:
593:
563:
503:
476:
449:
422:
371:
312:
278:
245:
173:
1643:Handbook of Econometrics Vol.1 Econometric Theory
1125:In practice, cointegration is often used for two
1740:. Cambridge University Press. pp. 155â248.
1737:Unit Roots, Cointegration, and Structural Change
1297:
1295:
199:in 1926. Before the 1980s, many economists used
3246:Multivariate adaptive regression splines (MARS)
1407:Engle, Robert F.; Granger, Clive W. J. (1987).
847:and the lagged residuals from the first stage,
126:. In an influential paper, Charles Nelson and
1801:
1682:(Second ed.). New York: Wiley. pp.
8:
1565:Gregory, Allan W.; Hansen, Bruce E. (1996).
1782:An intuitive introduction to cointegration.
1673:"Cointegration and Error-Correction Models"
889:. The second stage regression is given as:
3855:
3842:
3759:
3565:
3434:
3409:
3180:
3156:
2884:
2667:
2468:
2455:
2238:
2225:
1864:
1855:
1842:
1808:
1794:
1786:
1521:Phillips, P. C. B.; Ouliaris, S. (1990).
1505:
1317:
1132:
1074:
1058:
1042:
1033:
1007:
986:
980:
957:
938:
919:
903:
894:
867:
856:
855:
852:
831:
822:
801:
792:
769:
748:
742:
721:
715:
694:
688:
664:
635:
629:
609:
585:
579:
564:{\displaystyle y_{t}-\beta x_{t}=u_{t}\,}
560:
554:
541:
525:
519:
495:
489:
469:
441:
435:
414:
408:
355:
296:
262:
229:
157:
110:is integrated of order less than d, then
1646:. Palgrave Macmillan. pp. 871â898.
1257:Journal of the Royal Statistical Society
138:If two or more series are individually
1712:. Princeton University Press. pp.
1217:
3772:KaplanâMeier estimator (product limit)
1464:"ARDL Models - Part II - Bounds Tests"
1028:and we estimate a differences model:
7:
4082:
3782:Accelerated failure time (AFT) model
1106:PhillipsâOuliaris cointegration test
142:(in the time series sense) but some
4094:
3377:Analysis of variance (ANOVA, anova)
1166:Variable shifts in long time series
3472:CochranâMantelâHaenszel statistics
2098:Pearson product-moment correlation
1051:
1035:
912:
896:
824:
794:
14:
4093:
4081:
4069:
4056:
4055:
1679:Applied Econometrics Time Series
882:{\displaystyle {\hat {u}}_{t-1}}
3731:Least-squares spectral analysis
1486:Journal of Applied Econometrics
84:, and there exist coefficients
80:) are each integrated of order
2712:Mean-unbiased minimum-variance
1778:10.1080/00031305.1994.10476017
1143:
1137:
861:
366:
360:
307:
301:
273:
267:
240:
234:
168:
162:
1:
4025:Geographic information system
3241:Simultaneous equations models
1462:Giles, David (19 June 2013).
1228:Journal of Monetary Economics
393:EngleâGranger two-step method
187:linear combination of them.
3208:Coefficient of determination
2819:Uniformly most powerful test
1586:10.1016/0304-4076(69)41685-7
1394:10.1016/0304-4076(81)90079-8
1328:10.1016/0304-4076(74)90034-7
1241:10.1016/0304-3932(82)90012-5
1207:Stationary subspace analysis
840:{\displaystyle \Delta x_{t}}
810:{\displaystyle \Delta y_{t}}
653:Augmented DickeyâFuller test
3777:Proportional hazards models
3721:Spectral density estimation
3703:Vector autoregression (VAR)
3137:Maximum posterior estimator
2369:Randomized controlled trial
1755:Murray, Michael P. (1994).
4143:
3537:Multivariate distributions
1957:Average absolute deviation
817:on the lagged regressors,
396:
4051:
3854:
3841:
3525:Structural equation model
3433:
3408:
3179:
3155:
2887:
2861:Score/Lagrange multiplier
2467:
2454:
2276:Sample size determination
2237:
2224:
1854:
1841:
1823:
1765:The American Statistician
1619:10.1007/s00181-007-0175-9
1102:Distributed Lags (ARDL).
1021:{\displaystyle \alpha =0}
651:for stationarity with an
26:property of a collection
4020:Environmental statistics
3542:Elliptical distributions
3335:Generalized linear model
3264:Simple linear regression
3034:HodgesâLehmann estimator
2491:Probability distribution
2400:Stochastic approximation
1962:Coefficient of variation
3680:Cross-correlation (XCF)
3288:Non-standard predictors
2722:LehmannâScheffĂ© theorem
2395:Adaptive clinical trial
1670:Enders, Walter (2004).
1574:Journal of Econometrics
1381:Journal of Econometrics
1305:Journal of Econometrics
4076:Mathematics portal
3897:Engineering statistics
3805:NelsonâAalen estimator
3382:Analysis of covariance
3269:Ordinary least squares
3193:Pearson product-moment
2597:Statistical functional
2508:Empirical distribution
2341:Controlled experiments
2070:Frequency distribution
1848:Descriptive statistics
1734:; Kim, In-Moo (1998).
1197:Error correction model
1150:
1084:
1022:
996:
967:
883:
841:
811:
778:
777:{\displaystyle \beta }
758:
731:
704:
681:ordinary least squares
673:
672:{\displaystyle \beta }
645:
624:is known, we can test
618:
617:{\displaystyle \beta }
595:
565:
505:
478:
477:{\displaystyle \beta }
451:
424:
373:
331:ordinary least squares
314:
280:
247:
175:
3992:Population statistics
3934:System identification
3668:Autocorrelation (ACF)
3596:Exponential smoothing
3510:Discriminant analysis
3505:Canonical correlation
3369:Partition of variance
3231:Regression validation
3075:(JonckheereâTerpstra)
2974:Likelihood-ratio test
2663:Frequentist inference
2575:Locationâscale family
2496:Sampling distribution
2461:Statistical inference
2428:Cross-sectional study
2415:Observational studies
2374:Randomized experiment
2203:Stem-and-leaf display
2005:Central limit theorem
1599:Hatemi-J, A. (2008).
1151:
1085:
1023:
997:
995:{\displaystyle u_{t}}
968:
884:
842:
812:
779:
759:
757:{\displaystyle u_{t}}
732:
730:{\displaystyle x_{t}}
705:
703:{\displaystyle y_{t}}
674:
646:
644:{\displaystyle u_{t}}
619:
596:
594:{\displaystyle u_{t}}
566:
506:
504:{\displaystyle u_{t}}
479:
452:
450:{\displaystyle y_{t}}
425:
423:{\displaystyle x_{t}}
374:
315:
281:
248:
176:
4122:Mathematical finance
3915:Probabilistic design
3500:Principal components
3343:Exponential families
3295:Nonlinear regression
3274:General linear model
3236:Mixed effects models
3226:Errors and residuals
3203:Confounding variable
3105:Bayesian probability
3083:Van der Waerden test
3073:Ordered alternative
2838:Multiple comparisons
2717:RaoâBlackwellization
2680:Estimating equations
2636:Statistical distance
2354:Factorial experiment
1887:Arithmetic-Geometric
1149:{\displaystyle I(1)}
1131:
1111:Peter C. B. Phillips
1032:
1006:
979:
893:
851:
821:
791:
768:
741:
714:
687:
663:
657:PhillipsâPerron test
628:
608:
578:
518:
488:
468:
459:order of integration
434:
407:
372:{\displaystyle I(1)}
354:
313:{\displaystyle I(1)}
295:
279:{\displaystyle I(1)}
261:
246:{\displaystyle I(1)}
228:
213:spurious correlation
174:{\displaystyle I(1)}
156:
148:order of integration
146:of them has a lower
3987:Official statistics
3910:Methods engineering
3591:Seasonal adjustment
3359:Poisson regressions
3279:Bayesian regression
3218:Regression analysis
3198:Partial correlation
3170:Regression analysis
2769:Prediction interval
2764:Likelihood interval
2754:Confidence interval
2746:Interval estimation
2707:Unbiased estimators
2525:Model specification
2405:Up-and-down designs
2093:Partial correlation
2049:Index of dispersion
1967:Interquartile range
1606:Empirical Economics
511:. In other words:
346:spurious regression
4007:Spatial statistics
3887:Medical statistics
3787:First hitting time
3741:Whittle likelihood
3392:Degrees of freedom
3387:Multivariate ANOVA
3320:Heteroscedasticity
3132:Bayesian estimator
3097:Bayesian inference
2946:KolmogorovâSmirnov
2831:Randomization test
2801:Testing hypotheses
2774:Tolerance interval
2685:Maximum likelihood
2580:Exponential family
2513:Density estimation
2473:Statistical theory
2433:Natural experiment
2379:Scientific control
2296:Survey methodology
1982:Standard deviation
1357:10.1002/wilm.10167
1179:Bayesian inference
1160:Multicointegration
1146:
1121:Multicointegration
1080:
1018:
992:
963:
879:
837:
807:
774:
754:
727:
700:
669:
641:
614:
591:
561:
501:
474:
447:
420:
369:
344:). This is called
310:
276:
243:
201:linear regressions
171:
144:linear combination
66:linear combination
4109:
4108:
4047:
4046:
4043:
4042:
3982:National accounts
3952:Actuarial science
3944:Social statistics
3837:
3836:
3833:
3832:
3829:
3828:
3764:Survival function
3749:
3748:
3611:Granger causality
3452:Contingency table
3427:Survival analysis
3404:
3403:
3400:
3399:
3256:Linear regression
3151:
3150:
3147:
3146:
3122:Credible interval
3091:
3090:
2874:
2873:
2690:Method of moments
2559:Parametric family
2520:Statistical model
2450:
2449:
2446:
2445:
2364:Random assignment
2286:Statistical power
2220:
2219:
2216:
2215:
2065:Contingency table
2035:
2034:
1902:Generalized/power
1747:978-0-521-58782-2
1723:978-0-691-01018-2
1693:978-0-471-23065-6
1653:978-1-4039-4155-8
1202:Granger causality
864:
348:: two integrated
42:, ...,
4134:
4097:
4096:
4085:
4084:
4074:
4073:
4059:
4058:
3962:Crime statistics
3856:
3843:
3760:
3726:Fourier analysis
3713:Frequency domain
3693:
3640:
3606:Structural break
3566:
3515:Cluster analysis
3462:Log-linear model
3435:
3410:
3351:
3325:Homoscedasticity
3181:
3157:
3076:
3068:
3060:
3059:(KruskalâWallis)
3044:
3029:
2984:Cross validation
2969:
2951:AndersonâDarling
2898:
2885:
2856:Likelihood-ratio
2848:Parametric tests
2826:Permutation test
2809:1- & 2-tails
2700:Minimum distance
2672:Point estimation
2668:
2619:Optimal decision
2570:
2469:
2456:
2438:Quasi-experiment
2388:Adaptive designs
2239:
2226:
2103:Rank correlation
1865:
1856:
1843:
1810:
1803:
1796:
1787:
1781:
1761:
1751:
1727:
1711:
1697:
1675:
1658:
1657:
1637:
1631:
1630:
1596:
1590:
1589:
1571:
1562:
1556:
1555:
1527:
1518:
1512:
1511:
1509:
1481:
1475:
1474:
1472:
1470:
1459:
1453:
1448:
1442:
1441:
1413:
1404:
1398:
1397:
1375:
1369:
1368:
1338:
1332:
1331:
1321:
1299:
1290:
1289:
1251:
1245:
1244:
1222:
1185:Bayesian methods
1173:structural break
1157:
1155:
1153:
1152:
1147:
1089:
1087:
1086:
1081:
1079:
1078:
1063:
1062:
1047:
1046:
1027:
1025:
1024:
1019:
1001:
999:
998:
993:
991:
990:
972:
970:
969:
964:
962:
961:
949:
948:
924:
923:
908:
907:
888:
886:
885:
880:
878:
877:
866:
865:
857:
846:
844:
843:
838:
836:
835:
816:
814:
813:
808:
806:
805:
783:
781:
780:
775:
764:. However, when
763:
761:
760:
755:
753:
752:
736:
734:
733:
728:
726:
725:
709:
707:
706:
701:
699:
698:
678:
676:
675:
670:
650:
648:
647:
642:
640:
639:
623:
621:
620:
615:
600:
598:
597:
592:
590:
589:
570:
568:
567:
562:
559:
558:
546:
545:
530:
529:
510:
508:
507:
502:
500:
499:
483:
481:
480:
475:
456:
454:
453:
448:
446:
445:
429:
427:
426:
421:
419:
418:
380:
378:
376:
375:
370:
321:
319:
317:
316:
311:
287:
285:
283:
282:
277:
254:
252:
250:
249:
244:
182:
180:
178:
177:
172:
109:
52:
4142:
4141:
4137:
4136:
4135:
4133:
4132:
4131:
4112:
4111:
4110:
4105:
4068:
4039:
4001:
3938:
3924:quality control
3891:
3873:Clinical trials
3850:
3825:
3809:
3797:Hazard function
3791:
3745:
3707:
3691:
3654:
3650:BreuschâGodfrey
3638:
3615:
3555:
3530:Factor analysis
3476:
3457:Graphical model
3429:
3396:
3363:
3349:
3329:
3283:
3250:
3212:
3175:
3174:
3143:
3087:
3074:
3066:
3058:
3042:
3027:
3006:Rank statistics
3000:
2979:Model selection
2967:
2925:Goodness of fit
2919:
2896:
2870:
2842:
2795:
2740:
2729:Median unbiased
2657:
2568:
2501:Order statistic
2463:
2442:
2409:
2383:
2335:
2290:
2233:
2231:Data collection
2212:
2124:
2079:
2053:
2031:
1991:
1943:
1860:Continuous data
1850:
1837:
1819:
1814:
1759:
1754:
1748:
1730:
1724:
1700:
1694:
1669:
1666:
1664:Further reading
1661:
1654:
1639:
1638:
1634:
1598:
1597:
1593:
1569:
1564:
1563:
1559:
1544:10.2307/2938339
1525:
1520:
1519:
1515:
1498:10.1002/jae.616
1483:
1482:
1478:
1468:
1466:
1461:
1460:
1456:
1449:
1445:
1430:10.2307/1913236
1411:
1406:
1405:
1401:
1377:
1376:
1372:
1340:
1339:
1335:
1319:10.1.1.353.2946
1301:
1300:
1293:
1270:10.2307/2341482
1253:
1252:
1248:
1224:
1223:
1219:
1215:
1193:
1181:
1168:
1129:
1128:
1126:
1123:
1108:
1095:
1070:
1054:
1038:
1030:
1029:
1004:
1003:
982:
977:
976:
953:
934:
915:
899:
891:
890:
854:
849:
848:
827:
819:
818:
797:
789:
788:
766:
765:
744:
739:
738:
717:
712:
711:
690:
685:
684:
683:(by regressing
661:
660:
631:
626:
625:
606:
605:
601:is stationary.
581:
576:
575:
550:
537:
521:
516:
515:
491:
486:
485:
466:
465:
437:
432:
431:
410:
405:
404:
401:
395:
387:
352:
351:
349:
293:
292:
290:
259:
258:
256:
226:
225:
223:
222:For integrated
193:
154:
153:
151:
136:
128:Charles Plosser
97:
50:
41:
34:
27:
17:
12:
11:
5:
4140:
4138:
4130:
4129:
4124:
4114:
4113:
4107:
4106:
4104:
4103:
4091:
4079:
4065:
4052:
4049:
4048:
4045:
4044:
4041:
4040:
4038:
4037:
4032:
4027:
4022:
4017:
4011:
4009:
4003:
4002:
4000:
3999:
3994:
3989:
3984:
3979:
3974:
3969:
3964:
3959:
3954:
3948:
3946:
3940:
3939:
3937:
3936:
3931:
3926:
3917:
3912:
3907:
3901:
3899:
3893:
3892:
3890:
3889:
3884:
3879:
3870:
3868:Bioinformatics
3864:
3862:
3852:
3851:
3846:
3839:
3838:
3835:
3834:
3831:
3830:
3827:
3826:
3824:
3823:
3817:
3815:
3811:
3810:
3808:
3807:
3801:
3799:
3793:
3792:
3790:
3789:
3784:
3779:
3774:
3768:
3766:
3757:
3751:
3750:
3747:
3746:
3744:
3743:
3738:
3733:
3728:
3723:
3717:
3715:
3709:
3708:
3706:
3705:
3700:
3695:
3687:
3682:
3677:
3676:
3675:
3673:partial (PACF)
3664:
3662:
3656:
3655:
3653:
3652:
3647:
3642:
3634:
3629:
3623:
3621:
3620:Specific tests
3617:
3616:
3614:
3613:
3608:
3603:
3598:
3593:
3588:
3583:
3578:
3572:
3570:
3563:
3557:
3556:
3554:
3553:
3552:
3551:
3550:
3549:
3534:
3533:
3532:
3522:
3520:Classification
3517:
3512:
3507:
3502:
3497:
3492:
3486:
3484:
3478:
3477:
3475:
3474:
3469:
3467:McNemar's test
3464:
3459:
3454:
3449:
3443:
3441:
3431:
3430:
3413:
3406:
3405:
3402:
3401:
3398:
3397:
3395:
3394:
3389:
3384:
3379:
3373:
3371:
3365:
3364:
3362:
3361:
3345:
3339:
3337:
3331:
3330:
3328:
3327:
3322:
3317:
3312:
3307:
3305:Semiparametric
3302:
3297:
3291:
3289:
3285:
3284:
3282:
3281:
3276:
3271:
3266:
3260:
3258:
3252:
3251:
3249:
3248:
3243:
3238:
3233:
3228:
3222:
3220:
3214:
3213:
3211:
3210:
3205:
3200:
3195:
3189:
3187:
3177:
3176:
3173:
3172:
3167:
3161:
3160:
3153:
3152:
3149:
3148:
3145:
3144:
3142:
3141:
3140:
3139:
3129:
3124:
3119:
3118:
3117:
3112:
3101:
3099:
3093:
3092:
3089:
3088:
3086:
3085:
3080:
3079:
3078:
3070:
3062:
3046:
3043:(MannâWhitney)
3038:
3037:
3036:
3023:
3022:
3021:
3010:
3008:
3002:
3001:
2999:
2998:
2997:
2996:
2991:
2986:
2976:
2971:
2968:(ShapiroâWilk)
2963:
2958:
2953:
2948:
2943:
2935:
2929:
2927:
2921:
2920:
2918:
2917:
2909:
2900:
2888:
2882:
2880:Specific tests
2876:
2875:
2872:
2871:
2869:
2868:
2863:
2858:
2852:
2850:
2844:
2843:
2841:
2840:
2835:
2834:
2833:
2823:
2822:
2821:
2811:
2805:
2803:
2797:
2796:
2794:
2793:
2792:
2791:
2786:
2776:
2771:
2766:
2761:
2756:
2750:
2748:
2742:
2741:
2739:
2738:
2733:
2732:
2731:
2726:
2725:
2724:
2719:
2704:
2703:
2702:
2697:
2692:
2687:
2676:
2674:
2665:
2659:
2658:
2656:
2655:
2650:
2645:
2644:
2643:
2633:
2628:
2627:
2626:
2616:
2615:
2614:
2609:
2604:
2594:
2589:
2584:
2583:
2582:
2577:
2572:
2556:
2555:
2554:
2549:
2544:
2534:
2533:
2532:
2527:
2517:
2516:
2515:
2505:
2504:
2503:
2493:
2488:
2483:
2477:
2475:
2465:
2464:
2459:
2452:
2451:
2448:
2447:
2444:
2443:
2441:
2440:
2435:
2430:
2425:
2419:
2417:
2411:
2410:
2408:
2407:
2402:
2397:
2391:
2389:
2385:
2384:
2382:
2381:
2376:
2371:
2366:
2361:
2356:
2351:
2345:
2343:
2337:
2336:
2334:
2333:
2331:Standard error
2328:
2323:
2318:
2317:
2316:
2311:
2300:
2298:
2292:
2291:
2289:
2288:
2283:
2278:
2273:
2268:
2263:
2261:Optimal design
2258:
2253:
2247:
2245:
2235:
2234:
2229:
2222:
2221:
2218:
2217:
2214:
2213:
2211:
2210:
2205:
2200:
2195:
2190:
2185:
2180:
2175:
2170:
2165:
2160:
2155:
2150:
2145:
2140:
2134:
2132:
2126:
2125:
2123:
2122:
2117:
2116:
2115:
2110:
2100:
2095:
2089:
2087:
2081:
2080:
2078:
2077:
2072:
2067:
2061:
2059:
2058:Summary tables
2055:
2054:
2052:
2051:
2045:
2043:
2037:
2036:
2033:
2032:
2030:
2029:
2028:
2027:
2022:
2017:
2007:
2001:
1999:
1993:
1992:
1990:
1989:
1984:
1979:
1974:
1969:
1964:
1959:
1953:
1951:
1945:
1944:
1942:
1941:
1936:
1931:
1930:
1929:
1924:
1919:
1914:
1909:
1904:
1899:
1894:
1892:Contraharmonic
1889:
1884:
1873:
1871:
1862:
1852:
1851:
1846:
1839:
1838:
1836:
1835:
1830:
1824:
1821:
1820:
1815:
1813:
1812:
1805:
1798:
1790:
1784:
1783:
1752:
1746:
1732:Maddala, G. S.
1728:
1722:
1702:Hayashi, Fumio
1698:
1692:
1665:
1662:
1660:
1659:
1652:
1632:
1613:(3): 497â505.
1591:
1557:
1538:(1): 165â193.
1513:
1492:(3): 289â326.
1476:
1454:
1443:
1424:(2): 251â276.
1399:
1388:(1): 121â130.
1370:
1333:
1312:(2): 111â120.
1291:
1246:
1235:(2): 139â162.
1216:
1214:
1211:
1210:
1209:
1204:
1199:
1192:
1189:
1180:
1177:
1167:
1164:
1145:
1142:
1139:
1136:
1122:
1119:
1107:
1104:
1094:
1091:
1077:
1073:
1069:
1066:
1061:
1057:
1053:
1050:
1045:
1041:
1037:
1017:
1014:
1011:
989:
985:
960:
956:
952:
947:
944:
941:
937:
933:
930:
927:
922:
918:
914:
911:
906:
902:
898:
876:
873:
870:
863:
860:
834:
830:
826:
804:
800:
796:
773:
751:
747:
724:
720:
697:
693:
668:
638:
634:
613:
588:
584:
572:
571:
557:
553:
549:
544:
540:
536:
533:
528:
524:
498:
494:
473:
444:
440:
417:
413:
394:
391:
386:
383:
368:
365:
362:
359:
309:
306:
303:
300:
275:
272:
269:
266:
242:
239:
236:
233:
192:
189:
170:
167:
164:
161:
135:
132:
46:
39:
32:
15:
13:
10:
9:
6:
4:
3:
2:
4139:
4128:
4125:
4123:
4120:
4119:
4117:
4102:
4101:
4092:
4090:
4089:
4080:
4078:
4077:
4072:
4066:
4064:
4063:
4054:
4053:
4050:
4036:
4033:
4031:
4030:Geostatistics
4028:
4026:
4023:
4021:
4018:
4016:
4013:
4012:
4010:
4008:
4004:
3998:
3997:Psychometrics
3995:
3993:
3990:
3988:
3985:
3983:
3980:
3978:
3975:
3973:
3970:
3968:
3965:
3963:
3960:
3958:
3955:
3953:
3950:
3949:
3947:
3945:
3941:
3935:
3932:
3930:
3927:
3925:
3921:
3918:
3916:
3913:
3911:
3908:
3906:
3903:
3902:
3900:
3898:
3894:
3888:
3885:
3883:
3880:
3878:
3874:
3871:
3869:
3866:
3865:
3863:
3861:
3860:Biostatistics
3857:
3853:
3849:
3844:
3840:
3822:
3821:Log-rank test
3819:
3818:
3816:
3812:
3806:
3803:
3802:
3800:
3798:
3794:
3788:
3785:
3783:
3780:
3778:
3775:
3773:
3770:
3769:
3767:
3765:
3761:
3758:
3756:
3752:
3742:
3739:
3737:
3734:
3732:
3729:
3727:
3724:
3722:
3719:
3718:
3716:
3714:
3710:
3704:
3701:
3699:
3696:
3694:
3692:(BoxâJenkins)
3688:
3686:
3683:
3681:
3678:
3674:
3671:
3670:
3669:
3666:
3665:
3663:
3661:
3657:
3651:
3648:
3646:
3645:DurbinâWatson
3643:
3641:
3635:
3633:
3630:
3628:
3627:DickeyâFuller
3625:
3624:
3622:
3618:
3612:
3609:
3607:
3604:
3602:
3601:Cointegration
3599:
3597:
3594:
3592:
3589:
3587:
3584:
3582:
3579:
3577:
3576:Decomposition
3574:
3573:
3571:
3567:
3564:
3562:
3558:
3548:
3545:
3544:
3543:
3540:
3539:
3538:
3535:
3531:
3528:
3527:
3526:
3523:
3521:
3518:
3516:
3513:
3511:
3508:
3506:
3503:
3501:
3498:
3496:
3493:
3491:
3488:
3487:
3485:
3483:
3479:
3473:
3470:
3468:
3465:
3463:
3460:
3458:
3455:
3453:
3450:
3448:
3447:Cohen's kappa
3445:
3444:
3442:
3440:
3436:
3432:
3428:
3424:
3420:
3416:
3411:
3407:
3393:
3390:
3388:
3385:
3383:
3380:
3378:
3375:
3374:
3372:
3370:
3366:
3360:
3356:
3352:
3346:
3344:
3341:
3340:
3338:
3336:
3332:
3326:
3323:
3321:
3318:
3316:
3313:
3311:
3308:
3306:
3303:
3301:
3300:Nonparametric
3298:
3296:
3293:
3292:
3290:
3286:
3280:
3277:
3275:
3272:
3270:
3267:
3265:
3262:
3261:
3259:
3257:
3253:
3247:
3244:
3242:
3239:
3237:
3234:
3232:
3229:
3227:
3224:
3223:
3221:
3219:
3215:
3209:
3206:
3204:
3201:
3199:
3196:
3194:
3191:
3190:
3188:
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3084:
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3077:
3071:
3069:
3063:
3061:
3055:
3054:
3053:
3050:
3049:Nonparametric
3047:
3045:
3039:
3035:
3032:
3031:
3030:
3024:
3020:
3019:Sample median
3017:
3016:
3015:
3012:
3011:
3009:
3007:
3003:
2995:
2992:
2990:
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2899:
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2762:
2760:
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2747:
2743:
2737:
2734:
2730:
2727:
2723:
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2718:
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2710:
2709:
2708:
2705:
2701:
2698:
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2682:
2681:
2678:
2677:
2675:
2673:
2669:
2666:
2664:
2660:
2654:
2651:
2649:
2646:
2642:
2639:
2638:
2637:
2634:
2632:
2629:
2625:
2624:loss function
2622:
2621:
2620:
2617:
2613:
2610:
2608:
2605:
2603:
2600:
2599:
2598:
2595:
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2590:
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2585:
2581:
2578:
2576:
2573:
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2565:
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2560:
2557:
2553:
2550:
2548:
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2526:
2523:
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2514:
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2509:
2506:
2502:
2499:
2498:
2497:
2494:
2492:
2489:
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2479:
2478:
2476:
2474:
2470:
2466:
2462:
2457:
2453:
2439:
2436:
2434:
2431:
2429:
2426:
2424:
2421:
2420:
2418:
2416:
2412:
2406:
2403:
2401:
2398:
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2390:
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2380:
2377:
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2365:
2362:
2360:
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2355:
2352:
2350:
2347:
2346:
2344:
2342:
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2332:
2329:
2327:
2326:Questionnaire
2324:
2322:
2319:
2315:
2312:
2310:
2307:
2306:
2305:
2302:
2301:
2299:
2297:
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2269:
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2264:
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2259:
2257:
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2246:
2244:
2240:
2236:
2232:
2227:
2223:
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2206:
2204:
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2199:
2196:
2194:
2191:
2189:
2186:
2184:
2181:
2179:
2176:
2174:
2171:
2169:
2166:
2164:
2161:
2159:
2156:
2154:
2153:Control chart
2151:
2149:
2146:
2144:
2141:
2139:
2136:
2135:
2133:
2131:
2127:
2121:
2118:
2114:
2111:
2109:
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2105:
2104:
2101:
2099:
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2090:
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2076:
2073:
2071:
2068:
2066:
2063:
2062:
2060:
2056:
2050:
2047:
2046:
2044:
2042:
2038:
2026:
2023:
2021:
2018:
2016:
2013:
2012:
2011:
2008:
2006:
2003:
2002:
2000:
1998:
1994:
1988:
1985:
1983:
1980:
1978:
1975:
1973:
1970:
1968:
1965:
1963:
1960:
1958:
1955:
1954:
1952:
1950:
1946:
1940:
1937:
1935:
1932:
1928:
1925:
1923:
1920:
1918:
1915:
1913:
1910:
1908:
1905:
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1900:
1898:
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1866:
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1857:
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1849:
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1826:
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1818:
1811:
1806:
1804:
1799:
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1758:
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1733:
1729:
1725:
1719:
1715:
1710:
1709:
1703:
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1668:
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1663:
1655:
1649:
1645:
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1636:
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1624:
1620:
1616:
1612:
1608:
1607:
1602:
1595:
1592:
1587:
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1580:(1): 99â126.
1579:
1575:
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1561:
1558:
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1549:
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1345:
1337:
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1320:
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1306:
1298:
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1279:
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1263:
1259:
1258:
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1247:
1242:
1238:
1234:
1230:
1229:
1221:
1218:
1212:
1208:
1205:
1203:
1200:
1198:
1195:
1194:
1190:
1188:
1186:
1178:
1176:
1174:
1165:
1163:
1161:
1140:
1134:
1120:
1118:
1116:
1112:
1105:
1103:
1100:
1099:Johansen test
1093:Johansen test
1092:
1090:
1075:
1071:
1067:
1064:
1059:
1055:
1048:
1043:
1039:
1015:
1012:
1009:
987:
983:
973:
958:
954:
950:
945:
942:
939:
935:
931:
928:
925:
920:
916:
909:
904:
900:
874:
871:
868:
858:
832:
828:
802:
798:
785:
771:
749:
745:
722:
718:
695:
691:
682:
666:
658:
654:
636:
632:
611:
602:
586:
582:
555:
551:
547:
542:
538:
534:
531:
526:
522:
514:
513:
512:
496:
492:
471:
463:
460:
442:
438:
415:
411:
400:
392:
390:
384:
382:
363:
357:
347:
343:
339:
334:
332:
328:
323:
304:
298:
270:
264:
237:
231:
220:
218:
214:
210:
206:
205:Clive Granger
202:
198:
190:
188:
186:
165:
159:
149:
145:
141:
133:
131:
129:
125:
121:
117:
113:
108:
105: +
104:
101: +
100:
95:
91:
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79:
75:
71:
67:
64:. Next, if a
63:
60:
56:
49:
45:
38:
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25:
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20:Cointegration
4098:
4086:
4067:
4060:
3972:Econometrics
3922: /
3905:Chemometrics
3882:Epidemiology
3875: /
3848:Applications
3690:ARIMA model
3637:Q-statistic
3600:
3586:Stationarity
3482:Multivariate
3425: /
3421: /
3419:Multivariate
3417: /
3357: /
3353: /
3127:Bayes factor
3026:Signed rank
2938:
2912:
2904:
2892:
2587:Completeness
2423:Cohort study
2321:Opinion poll
2256:Missing data
2243:Study design
2198:Scatter plot
2120:Scatter plot
2113:Spearman's Ï
2075:Grouped data
1772:(1): 37â39.
1769:
1763:
1736:
1708:Econometrics
1707:
1678:
1642:
1635:
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1604:
1594:
1577:
1573:
1560:
1535:
1531:Econometrica
1529:
1516:
1489:
1485:
1479:
1467:. Retrieved
1457:
1446:
1421:
1417:Econometrica
1415:
1402:
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1379:
1373:
1351:(1): 64â73.
1348:
1342:
1336:
1309:
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1264:(1): 11â63.
1261:
1255:
1249:
1232:
1226:
1220:
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1169:
1159:
1124:
1115:Sam Ouliaris
1109:
1096:
974:
786:
603:
573:
461:
402:
388:
335:
324:
221:
217:Robert Engle
209:Paul Newbold
194:
137:
134:Introduction
119:
115:
111:
106:
102:
98:
93:
89:
85:
81:
77:
73:
69:
61:
47:
43:
36:
29:
19:
18:
4127:Time series
4100:WikiProject
4015:Cartography
3977:Jurimetrics
3929:Reliability
3660:Time domain
3639:(LjungâBox)
3561:Time-series
3439:Categorical
3423:Time-series
3415:Categorical
3350:(Bernoulli)
3185:Correlation
3165:Correlation
2961:JarqueâBera
2933:Chi-squared
2695:M-estimator
2648:Asymptotics
2592:Sufficiency
2359:Interaction
2271:Replication
2251:Effect size
2208:Violin plot
2188:Radar chart
2168:Forest plot
2158:Correlogram
2108:Kendall's Ï
1507:10983/25617
55:time series
24:statistical
4116:Categories
3967:Demography
3685:ARMA model
3490:Regression
3067:(Friedman)
3028:(Wilcoxon)
2966:Normality
2956:Lilliefors
2903:Student's
2779:Resampling
2653:Robustness
2641:divergence
2631:Efficiency
2569:(monotone)
2564:Likelihood
2481:Population
2314:Stratified
2266:Population
2085:Dependence
2041:Count data
1972:Percentile
1949:Dispersion
1882:Arithmetic
1817:Statistics
1213:References
457:both have
397:See also:
327:unit roots
185:stationary
140:integrated
124:stochastic
96:such that
3348:Logistic
3115:posterior
3041:Rank sum
2789:Jackknife
2784:Bootstrap
2602:Bootstrap
2537:Parameter
2486:Statistic
2281:Statistic
2193:Run chart
2178:Pie chart
2173:Histogram
2163:Fan chart
2138:Bar chart
2020:L-moments
1907:Geometric
1627:153437469
1365:154550363
1314:CiteSeerX
1286:126346450
1072:ε
1052:Δ
1036:Δ
1010:α
955:ε
943:−
932:α
913:Δ
897:Δ
872:−
862:^
825:Δ
795:Δ
772:β
667:β
612:β
535:β
532:−
472:β
338:R-squared
197:Udny Yule
4062:Category
3755:Survival
3632:Johansen
3355:Binomial
3310:Isotonic
2897:(normal)
2542:location
2349:Blocking
2304:Sampling
2183:QâQ plot
2148:Box plot
2130:Graphics
2025:Skewness
2015:Kurtosis
1987:Variance
1917:Heronian
1912:Harmonic
1704:(2000).
1469:4 August
1191:See also
1183:Several
1002:), then
4088:Commons
4035:Kriging
3920:Process
3877:studies
3736:Wavelet
3569:General
2736:Plug-in
2530:L space
2309:Cluster
2010:Moments
1828:Outline
1684:319â386
1552:2938339
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1344:Wilmott
1278:2341482
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191:History
181:
152:
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3957:Census
3547:Normal
3495:Manova
3315:Robust
3065:2-way
3057:1-way
2895:-test
2566:
2143:Biplot
1934:Median
1927:Lehmer
1869:Center
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574:where
118:, and
3581:Trend
3110:prior
3052:anova
2941:-test
2915:-test
2907:-test
2814:Power
2759:Pivot
2552:shape
2547:scale
1997:Shape
1977:Range
1922:Heinz
1897:Cubic
1833:Index
1760:(PDF)
1623:S2CID
1570:(PDF)
1548:JSTOR
1526:(PDF)
1434:JSTOR
1412:(PDF)
1361:S2CID
1282:S2CID
1274:JSTOR
385:Tests
59:order
22:is a
3814:Test
3014:Sign
2866:Wald
1939:Mode
1877:Mean
1742:ISBN
1718:ISBN
1688:ISBN
1648:ISBN
1471:2014
1349:2012
1113:and
1097:The
484:and
430:and
207:and
2994:BIC
2989:AIC
1774:doi
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1582:doi
1540:doi
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1494:doi
1426:doi
1390:doi
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655:or
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