1128:(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.
4082:
4068:
4106:
4094:
1182:
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
1181:
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,
1112:
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
299:
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
982:
1099:
266:
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
580:
898:
1169:
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).
856:
826:
347:
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
1037:
336:
The possible presence of cointegration must be taken into account when choosing a technique to test hypotheses concerning the relationship between two variables having
793:
688:
633:
493:
1011:
773:
746:
719:
660:
610:
520:
466:
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1165:
388:
329:
295:
262:
190:
3203:
1651:
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.).
3708:
133:
are cointegrated. Cointegration has become an important property in contemporary time series analysis. Time series often have trendsâeither deterministic or
340:(i.e. integrated of at least order one). The usual procedure for testing hypotheses concerning the relationship between non-stationary variables was to run
3858:
3482:
2123:
3256:
1267:
3695:
1198:
have been proposed to compute the posterior distribution of the number of cointegrating relationships and the cointegrating linear combinations.
903:
1756:
1732:
1702:
1662:
2118:
1818:
1265:
Yule, U. (1926). "Why do we sometimes get nonsense-correlations between time series? - A study in sampling and the nature of time series".
1767:
2722:
1870:
141:(1982) provided statistical evidence that many US macroeconomic time series (like GNP, wages, employment, etc.) have stochastic trends.
795:
is estimated, the critical values of this ADF test are non-standard, and increase in absolute value as more regressors are included.
3505:
3397:
663:
4110:
3683:
3557:
1042:
3741:
3402:
3147:
2518:
2108:
2732:
344:(OLS) regressions on data which had been differenced. This method is biased if the non-stationary variables are cointegrated.
3792:
3004:
2811:
2700:
2658:
1897:
161:, then the series are said to be cointegrated. A common example is where the individual series are first-order integrated (
4132:
4035:
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1238:
3044:
3586:
3535:
3520:
3510:
3379:
3251:
3218:
2999:
2829:
1217:
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extends the cointegration technique beyond two variables, and occasionally to variables integrated at different orders.
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2956:
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2710:
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1843:
79:
of this collection is integrated of order less than d, then the collection is said to be co-integrated. Formally, if (
3815:
3782:
333:
series on both sides of the regression relationship, then it is possible for regressions to give misleading results.
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3289:
3195:
3175:
3083:
2794:
2612:
2095:
1967:
226:, since standard detrending techniques can result in data that are still non-stationary. Granger's 1987 paper with
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2286:
2007:
1775:
1495:
Pesaran, M.H.; Shin, Y.; Smith, R.J. (2001). "Bounds testing approaches to the analysis of level relationships".
1461:
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667:
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3059:
2501:
2410:
2369:
2281:
1972:
1811:
1389:
Granger, Clive (1981). "Some
Properties of Time Series Data and Their Use in Econometric Model Specification".
798:
If the variables are found to be cointegrated, a second-stage regression is conducted. This is a regression of
528:
3067:
3051:
1474:
3939:
3552:
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3429:
2789:
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2405:
1612:"Tests for cointegration with two unknown regime shifts with an application to financial market integration"
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2015:
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2020:
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If the variables are not cointegrated (if we cannot reject the null of no cointegration when testing
469:
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223:
158:
150:
69:
1329:
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1977:
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1992:
1987:
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195:
154:
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475:=1 and are cointegrated, then a linear combination of them must be stationary for some value of
1724:
1611:
1016:
392:
series which are not directly causally related may nonetheless show a significant correlation.
3992:
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1949:
1752:
1746:
1728:
1698:
1658:
1212:
211:
1352:
Mahdavi
Damghani, Babak; et al. (2012). "The Misleading Value of Measured Correlation".
4017:
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2562:
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2511:
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1892:
1236:
Nelson, C.R; Plosser, C.I (1982). "Trends and random walks in macroeconomic time series".
1141:
364:
305:
271:
238:
166:
138:
351:
relationship (suggesting high explanatory power on Fiji's consumption from
Afghanistan's
3883:
3878:
2341:
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1917:
1683:
206:
The first to introduce and analyse the concept of spuriousâor nonsenseâregression was
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2178:
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1937:
65:
34:
1419:
2871:
2351:
2051:
1982:
1932:
1907:
1827:
1629:
1462:
https://www.econ.queensu.ca/sites/econ.queensu.ca/files/wpaper/qed_wp_1227.pdf
134:
17:
1420:"Co-integration and error correction: Representation, estimation and testing"
3024:
2876:
2496:
2291:
2203:
2188:
2183:
2148:
1768:"A Drunk and her Dog: An Illustration of Cointegration and Error Correction"
348:
337:
207:
1652:
1186:, and tests for cointegration with two unknown breaks are also available.
977:{\displaystyle \Delta y_{t}=\Delta x_{t}b+\alpha u_{t-1}+\varepsilon _{t}}
2540:
2158:
2035:
2030:
2025:
1997:
1313:
Granger, C.; Newbold, P. (1974). "Spurious
Regressions in Econometrics".
4045:
3746:
1562:
1517:
1448:
1367:
1288:
690:
is unknown, we must first estimate it. This is typically done by using
3967:
2948:
2922:
2902:
2153:
1944:
1578:"Residual-based tests for cointegration in models with regime shifts"
1554:
1508:
1440:
1280:
230:
formalized the cointegrating vector approach, and coined the term.
194:) but some (cointegrating) vector of coefficients exists to form a
1534:"Asymptotic Properties of Residual Based Tests for Cointegration"
1887:
3856:
3423:
3170:
2469:
2239:
1856:
1800:
410:
Error correction model § Engle and
Granger 2-step approach
352:
1796:
1094:{\displaystyle \Delta y_{t}=\Delta x_{t}b+\varepsilon _{t}}
68:
variables. First, all of the series must be integrated of
214:
on non-stationary time series data, which Nobel laureate
400:
The six main methods for testing for cointegration are:
27:
Statistical property of collections of time series data
1144:
1045:
1019:
992:
906:
864:
834:
804:
781:
754:
727:
700:
676:
641:
621:
591:
531:
501:
481:
447:
420:
367:
308:
274:
241:
222:
showed to be a dangerous approach that could produce
169:
3709:
Autoregressive conditional heteroskedasticity (ARCH)
4016:
3953:
3906:
3869:
3824:
3806:
3773:
3764:
3722:
3669:
3630:
3579:
3570:
3491:
3448:
3378:
3344:
3298:
3265:
3227:
3194:
3106:
3015:
2934:
2889:
2857:
2810:
2755:
2681:
2672:
2482:
2424:
2398:
2350:
2305:
2252:
2139:
2094:
2068:
2050:
2006:
1958:
1878:
1869:
748:and an intercept). Then, we can run an ADF test on
1682:
1159:
1093:
1031:
1005:
976:
892:
850:
820:
787:
767:
740:
713:
682:
654:
627:
604:
574:
514:
487:
460:
433:
382:
323:
289:
256:
184:
1654:Handbook of Econometrics Vol.1 Econometric Theory
1136:In practice, cointegration is often used for two
1751:. Cambridge University Press. pp. 155â248.
1748:Unit Roots, Cointegration, and Structural Change
1308:
1306:
210:in 1926. Before the 1980s, many economists used
3257:Multivariate adaptive regression splines (MARS)
1418:Engle, Robert F.; Granger, Clive W. J. (1987).
858:and the lagged residuals from the first stage,
137:. In an influential paper, Charles Nelson and
1812:
1693:(Second ed.). New York: Wiley. pp.
8:
1576:Gregory, Allan W.; Hansen, Bruce E. (1996).
1793:An intuitive introduction to cointegration.
1684:"Cointegration and Error-Correction Models"
900:. The second stage regression is given as:
3866:
3853:
3770:
3576:
3445:
3420:
3191:
3167:
2895:
2678:
2479:
2466:
2249:
2236:
1875:
1866:
1853:
1819:
1805:
1797:
1532:Phillips, P. C. B.; Ouliaris, S. (1990).
1516:
1328:
1143:
1085:
1069:
1053:
1044:
1018:
997:
991:
968:
949:
930:
914:
905:
878:
867:
866:
863:
842:
833:
812:
803:
780:
759:
753:
732:
726:
705:
699:
675:
646:
640:
620:
596:
590:
575:{\displaystyle y_{t}-\beta x_{t}=u_{t}\,}
571:
565:
552:
536:
530:
506:
500:
480:
452:
446:
425:
419:
366:
307:
273:
240:
168:
121:is integrated of order less than d, then
1657:. Palgrave Macmillan. pp. 871â898.
1268:Journal of the Royal Statistical Society
149:If two or more series are individually
1723:. Princeton University Press. pp.
1228:
3783:KaplanâMeier estimator (product limit)
1475:"ARDL Models - Part II - Bounds Tests"
1039:and we estimate a differences model:
7:
4093:
3793:Accelerated failure time (AFT) model
1117:PhillipsâOuliaris cointegration test
153:(in the time series sense) but some
4105:
3388:Analysis of variance (ANOVA, anova)
1177:Variable shifts in long time series
3483:CochranâMantelâHaenszel statistics
2109:Pearson product-moment correlation
1062:
1046:
923:
907:
835:
805:
25:
4104:
4092:
4080:
4067:
4066:
1690:Applied Econometrics Time Series
893:{\displaystyle {\hat {u}}_{t-1}}
3742:Least-squares spectral analysis
1497:Journal of Applied Econometrics
95:, and there exist coefficients
91:) are each integrated of order
2723:Mean-unbiased minimum-variance
1789:10.1080/00031305.1994.10476017
1154:
1148:
872:
377:
371:
318:
312:
284:
278:
251:
245:
179:
173:
1:
4036:Geographic information system
3252:Simultaneous equations models
1473:Giles, David (19 June 2013).
1239:Journal of Monetary Economics
404:EngleâGranger two-step method
198:linear combination of them.
3219:Coefficient of determination
2830:Uniformly most powerful test
1597:10.1016/0304-4076(69)41685-7
1405:10.1016/0304-4076(81)90079-8
1339:10.1016/0304-4076(74)90034-7
1252:10.1016/0304-3932(82)90012-5
1218:Stationary subspace analysis
851:{\displaystyle \Delta x_{t}}
821:{\displaystyle \Delta y_{t}}
664:Augmented DickeyâFuller test
3788:Proportional hazards models
3732:Spectral density estimation
3714:Vector autoregression (VAR)
3148:Maximum posterior estimator
2380:Randomized controlled trial
1766:Murray, Michael P. (1994).
4154:
3548:Multivariate distributions
1968:Average absolute deviation
828:on the lagged regressors,
407:
4062:
3865:
3852:
3536:Structural equation model
3444:
3419:
3190:
3166:
2898:
2872:Score/Lagrange multiplier
2478:
2465:
2287:Sample size determination
2248:
2235:
1865:
1852:
1834:
1776:The American Statistician
1630:10.1007/s00181-007-0175-9
1113:Distributed Lags (ARDL).
1032:{\displaystyle \alpha =0}
662:for stationarity with an
37:property of a collection
4031:Environmental statistics
3553:Elliptical distributions
3346:Generalized linear model
3275:Simple linear regression
3045:HodgesâLehmann estimator
2502:Probability distribution
2411:Stochastic approximation
1973:Coefficient of variation
3691:Cross-correlation (XCF)
3299:Non-standard predictors
2733:LehmannâScheffĂ© theorem
2406:Adaptive clinical trial
1681:Enders, Walter (2004).
1585:Journal of Econometrics
1392:Journal of Econometrics
1316:Journal of Econometrics
4087:Mathematics portal
3908:Engineering statistics
3816:NelsonâAalen estimator
3393:Analysis of covariance
3280:Ordinary least squares
3204:Pearson product-moment
2608:Statistical functional
2519:Empirical distribution
2352:Controlled experiments
2081:Frequency distribution
1859:Descriptive statistics
1745:; Kim, In-Moo (1998).
1208:Error correction model
1161:
1095:
1033:
1007:
978:
894:
852:
822:
789:
788:{\displaystyle \beta }
769:
742:
715:
692:ordinary least squares
684:
683:{\displaystyle \beta }
656:
635:is known, we can test
629:
628:{\displaystyle \beta }
606:
576:
516:
489:
488:{\displaystyle \beta }
462:
435:
384:
342:ordinary least squares
325:
291:
258:
186:
4003:Population statistics
3945:System identification
3679:Autocorrelation (ACF)
3607:Exponential smoothing
3521:Discriminant analysis
3516:Canonical correlation
3380:Partition of variance
3242:Regression validation
3086:(JonckheereâTerpstra)
2985:Likelihood-ratio test
2674:Frequentist inference
2586:Locationâscale family
2507:Sampling distribution
2472:Statistical inference
2439:Cross-sectional study
2426:Observational studies
2385:Randomized experiment
2214:Stem-and-leaf display
2016:Central limit theorem
1610:Hatemi-J, A. (2008).
1162:
1096:
1034:
1008:
1006:{\displaystyle u_{t}}
979:
895:
853:
823:
790:
770:
768:{\displaystyle u_{t}}
743:
741:{\displaystyle x_{t}}
716:
714:{\displaystyle y_{t}}
685:
657:
655:{\displaystyle u_{t}}
630:
607:
605:{\displaystyle u_{t}}
577:
517:
515:{\displaystyle u_{t}}
490:
463:
461:{\displaystyle y_{t}}
436:
434:{\displaystyle x_{t}}
385:
326:
292:
259:
187:
4133:Mathematical finance
3926:Probabilistic design
3511:Principal components
3354:Exponential families
3306:Nonlinear regression
3285:General linear model
3247:Mixed effects models
3237:Errors and residuals
3214:Confounding variable
3116:Bayesian probability
3094:Van der Waerden test
3084:Ordered alternative
2849:Multiple comparisons
2728:RaoâBlackwellization
2691:Estimating equations
2647:Statistical distance
2365:Factorial experiment
1898:Arithmetic-Geometric
1160:{\displaystyle I(1)}
1142:
1122:Peter C. B. Phillips
1043:
1017:
990:
904:
862:
832:
802:
779:
752:
725:
698:
674:
668:PhillipsâPerron test
639:
619:
589:
529:
499:
479:
470:order of integration
445:
418:
383:{\displaystyle I(1)}
365:
324:{\displaystyle I(1)}
306:
290:{\displaystyle I(1)}
272:
257:{\displaystyle I(1)}
239:
224:spurious correlation
185:{\displaystyle I(1)}
167:
159:order of integration
157:of them has a lower
3998:Official statistics
3921:Methods engineering
3602:Seasonal adjustment
3370:Poisson regressions
3290:Bayesian regression
3229:Regression analysis
3209:Partial correlation
3181:Regression analysis
2780:Prediction interval
2775:Likelihood interval
2765:Confidence interval
2757:Interval estimation
2718:Unbiased estimators
2536:Model specification
2416:Up-and-down designs
2104:Partial correlation
2060:Index of dispersion
1978:Interquartile range
1617:Empirical Economics
522:. In other words:
357:spurious regression
4018:Spatial statistics
3898:Medical statistics
3798:First hitting time
3752:Whittle likelihood
3403:Degrees of freedom
3398:Multivariate ANOVA
3331:Heteroscedasticity
3143:Bayesian estimator
3108:Bayesian inference
2957:KolmogorovâSmirnov
2842:Randomization test
2812:Testing hypotheses
2785:Tolerance interval
2696:Maximum likelihood
2591:Exponential family
2524:Density estimation
2484:Statistical theory
2444:Natural experiment
2390:Scientific control
2307:Survey methodology
1993:Standard deviation
1368:10.1002/wilm.10167
1190:Bayesian inference
1171:Multicointegration
1157:
1132:Multicointegration
1091:
1029:
1003:
974:
890:
848:
818:
785:
765:
738:
711:
680:
652:
625:
602:
572:
512:
485:
458:
431:
380:
355:). This is called
321:
287:
254:
212:linear regressions
182:
155:linear combination
77:linear combination
4120:
4119:
4058:
4057:
4054:
4053:
3993:National accounts
3963:Actuarial science
3955:Social statistics
3848:
3847:
3844:
3843:
3840:
3839:
3775:Survival function
3760:
3759:
3622:Granger causality
3463:Contingency table
3438:Survival analysis
3415:
3414:
3411:
3410:
3267:Linear regression
3162:
3161:
3158:
3157:
3133:Credible interval
3102:
3101:
2885:
2884:
2701:Method of moments
2570:Parametric family
2531:Statistical model
2461:
2460:
2457:
2456:
2375:Random assignment
2297:Statistical power
2231:
2230:
2227:
2226:
2076:Contingency table
2046:
2045:
1913:Generalized/power
1758:978-0-521-58782-2
1734:978-0-691-01018-2
1704:978-0-471-23065-6
1664:978-1-4039-4155-8
1213:Granger causality
875:
359:: two integrated
53:, ...,
16:(Redirected from
4145:
4108:
4107:
4096:
4095:
4085:
4084:
4070:
4069:
3973:Crime statistics
3867:
3854:
3771:
3737:Fourier analysis
3724:Frequency domain
3704:
3651:
3617:Structural break
3577:
3526:Cluster analysis
3473:Log-linear model
3446:
3421:
3362:
3336:Homoscedasticity
3192:
3168:
3087:
3079:
3071:
3070:(KruskalâWallis)
3055:
3040:
2995:Cross validation
2980:
2962:AndersonâDarling
2909:
2896:
2867:Likelihood-ratio
2859:Parametric tests
2837:Permutation test
2820:1- & 2-tails
2711:Minimum distance
2683:Point estimation
2679:
2630:Optimal decision
2581:
2480:
2467:
2449:Quasi-experiment
2399:Adaptive designs
2250:
2237:
2114:Rank correlation
1876:
1867:
1854:
1821:
1814:
1807:
1798:
1792:
1772:
1762:
1738:
1722:
1708:
1686:
1669:
1668:
1648:
1642:
1641:
1607:
1601:
1600:
1582:
1573:
1567:
1566:
1538:
1529:
1523:
1522:
1520:
1492:
1486:
1485:
1483:
1481:
1470:
1464:
1459:
1453:
1452:
1424:
1415:
1409:
1408:
1386:
1380:
1379:
1349:
1343:
1342:
1332:
1310:
1301:
1300:
1262:
1256:
1255:
1233:
1196:Bayesian methods
1184:structural break
1168:
1166:
1164:
1163:
1158:
1100:
1098:
1097:
1092:
1090:
1089:
1074:
1073:
1058:
1057:
1038:
1036:
1035:
1030:
1012:
1010:
1009:
1004:
1002:
1001:
983:
981:
980:
975:
973:
972:
960:
959:
935:
934:
919:
918:
899:
897:
896:
891:
889:
888:
877:
876:
868:
857:
855:
854:
849:
847:
846:
827:
825:
824:
819:
817:
816:
794:
792:
791:
786:
775:. However, when
774:
772:
771:
766:
764:
763:
747:
745:
744:
739:
737:
736:
720:
718:
717:
712:
710:
709:
689:
687:
686:
681:
661:
659:
658:
653:
651:
650:
634:
632:
631:
626:
611:
609:
608:
603:
601:
600:
581:
579:
578:
573:
570:
569:
557:
556:
541:
540:
521:
519:
518:
513:
511:
510:
494:
492:
491:
486:
467:
465:
464:
459:
457:
456:
440:
438:
437:
432:
430:
429:
391:
389:
387:
386:
381:
332:
330:
328:
327:
322:
298:
296:
294:
293:
288:
265:
263:
261:
260:
255:
193:
191:
189:
188:
183:
120:
63:
21:
4153:
4152:
4148:
4147:
4146:
4144:
4143:
4142:
4123:
4122:
4121:
4116:
4079:
4050:
4012:
3949:
3935:quality control
3902:
3884:Clinical trials
3861:
3836:
3820:
3808:Hazard function
3802:
3756:
3718:
3702:
3665:
3661:BreuschâGodfrey
3649:
3626:
3566:
3541:Factor analysis
3487:
3468:Graphical model
3440:
3407:
3374:
3360:
3340:
3294:
3261:
3223:
3186:
3185:
3154:
3098:
3085:
3077:
3069:
3053:
3038:
3017:Rank statistics
3011:
2990:Model selection
2978:
2936:Goodness of fit
2930:
2907:
2881:
2853:
2806:
2751:
2740:Median unbiased
2668:
2579:
2512:Order statistic
2474:
2453:
2420:
2394:
2346:
2301:
2244:
2242:Data collection
2223:
2135:
2090:
2064:
2042:
2002:
1954:
1871:Continuous data
1861:
1848:
1830:
1825:
1770:
1765:
1759:
1741:
1735:
1711:
1705:
1680:
1677:
1675:Further reading
1672:
1665:
1650:
1649:
1645:
1609:
1608:
1604:
1580:
1575:
1574:
1570:
1555:10.2307/2938339
1536:
1531:
1530:
1526:
1509:10.1002/jae.616
1494:
1493:
1489:
1479:
1477:
1472:
1471:
1467:
1460:
1456:
1441:10.2307/1913236
1422:
1417:
1416:
1412:
1388:
1387:
1383:
1351:
1350:
1346:
1330:10.1.1.353.2946
1312:
1311:
1304:
1281:10.2307/2341482
1264:
1263:
1259:
1235:
1234:
1230:
1226:
1204:
1192:
1179:
1140:
1139:
1137:
1134:
1119:
1106:
1081:
1065:
1049:
1041:
1040:
1015:
1014:
993:
988:
987:
964:
945:
926:
910:
902:
901:
865:
860:
859:
838:
830:
829:
808:
800:
799:
777:
776:
755:
750:
749:
728:
723:
722:
701:
696:
695:
694:(by regressing
672:
671:
642:
637:
636:
617:
616:
612:is stationary.
592:
587:
586:
561:
548:
532:
527:
526:
502:
497:
496:
477:
476:
448:
443:
442:
421:
416:
415:
412:
406:
398:
363:
362:
360:
304:
303:
301:
270:
269:
267:
237:
236:
234:
233:For integrated
204:
165:
164:
162:
147:
139:Charles Plosser
108:
61:
52:
45:
38:
28:
23:
22:
15:
12:
11:
5:
4151:
4149:
4141:
4140:
4135:
4125:
4124:
4118:
4117:
4115:
4114:
4102:
4090:
4076:
4063:
4060:
4059:
4056:
4055:
4052:
4051:
4049:
4048:
4043:
4038:
4033:
4028:
4022:
4020:
4014:
4013:
4011:
4010:
4005:
4000:
3995:
3990:
3985:
3980:
3975:
3970:
3965:
3959:
3957:
3951:
3950:
3948:
3947:
3942:
3937:
3928:
3923:
3918:
3912:
3910:
3904:
3903:
3901:
3900:
3895:
3890:
3881:
3879:Bioinformatics
3875:
3873:
3863:
3862:
3857:
3850:
3849:
3846:
3845:
3842:
3841:
3838:
3837:
3835:
3834:
3828:
3826:
3822:
3821:
3819:
3818:
3812:
3810:
3804:
3803:
3801:
3800:
3795:
3790:
3785:
3779:
3777:
3768:
3762:
3761:
3758:
3757:
3755:
3754:
3749:
3744:
3739:
3734:
3728:
3726:
3720:
3719:
3717:
3716:
3711:
3706:
3698:
3693:
3688:
3687:
3686:
3684:partial (PACF)
3675:
3673:
3667:
3666:
3664:
3663:
3658:
3653:
3645:
3640:
3634:
3632:
3631:Specific tests
3628:
3627:
3625:
3624:
3619:
3614:
3609:
3604:
3599:
3594:
3589:
3583:
3581:
3574:
3568:
3567:
3565:
3564:
3563:
3562:
3561:
3560:
3545:
3544:
3543:
3533:
3531:Classification
3528:
3523:
3518:
3513:
3508:
3503:
3497:
3495:
3489:
3488:
3486:
3485:
3480:
3478:McNemar's test
3475:
3470:
3465:
3460:
3454:
3452:
3442:
3441:
3424:
3417:
3416:
3413:
3412:
3409:
3408:
3406:
3405:
3400:
3395:
3390:
3384:
3382:
3376:
3375:
3373:
3372:
3356:
3350:
3348:
3342:
3341:
3339:
3338:
3333:
3328:
3323:
3318:
3316:Semiparametric
3313:
3308:
3302:
3300:
3296:
3295:
3293:
3292:
3287:
3282:
3277:
3271:
3269:
3263:
3262:
3260:
3259:
3254:
3249:
3244:
3239:
3233:
3231:
3225:
3224:
3222:
3221:
3216:
3211:
3206:
3200:
3198:
3188:
3187:
3184:
3183:
3178:
3172:
3171:
3164:
3163:
3160:
3159:
3156:
3155:
3153:
3152:
3151:
3150:
3140:
3135:
3130:
3129:
3128:
3123:
3112:
3110:
3104:
3103:
3100:
3099:
3097:
3096:
3091:
3090:
3089:
3081:
3073:
3057:
3054:(MannâWhitney)
3049:
3048:
3047:
3034:
3033:
3032:
3021:
3019:
3013:
3012:
3010:
3009:
3008:
3007:
3002:
2997:
2987:
2982:
2979:(ShapiroâWilk)
2974:
2969:
2964:
2959:
2954:
2946:
2940:
2938:
2932:
2931:
2929:
2928:
2920:
2911:
2899:
2893:
2891:Specific tests
2887:
2886:
2883:
2882:
2880:
2879:
2874:
2869:
2863:
2861:
2855:
2854:
2852:
2851:
2846:
2845:
2844:
2834:
2833:
2832:
2822:
2816:
2814:
2808:
2807:
2805:
2804:
2803:
2802:
2797:
2787:
2782:
2777:
2772:
2767:
2761:
2759:
2753:
2752:
2750:
2749:
2744:
2743:
2742:
2737:
2736:
2735:
2730:
2715:
2714:
2713:
2708:
2703:
2698:
2687:
2685:
2676:
2670:
2669:
2667:
2666:
2661:
2656:
2655:
2654:
2644:
2639:
2638:
2637:
2627:
2626:
2625:
2620:
2615:
2605:
2600:
2595:
2594:
2593:
2588:
2583:
2567:
2566:
2565:
2560:
2555:
2545:
2544:
2543:
2538:
2528:
2527:
2526:
2516:
2515:
2514:
2504:
2499:
2494:
2488:
2486:
2476:
2475:
2470:
2463:
2462:
2459:
2458:
2455:
2454:
2452:
2451:
2446:
2441:
2436:
2430:
2428:
2422:
2421:
2419:
2418:
2413:
2408:
2402:
2400:
2396:
2395:
2393:
2392:
2387:
2382:
2377:
2372:
2367:
2362:
2356:
2354:
2348:
2347:
2345:
2344:
2342:Standard error
2339:
2334:
2329:
2328:
2327:
2322:
2311:
2309:
2303:
2302:
2300:
2299:
2294:
2289:
2284:
2279:
2274:
2272:Optimal design
2269:
2264:
2258:
2256:
2246:
2245:
2240:
2233:
2232:
2229:
2228:
2225:
2224:
2222:
2221:
2216:
2211:
2206:
2201:
2196:
2191:
2186:
2181:
2176:
2171:
2166:
2161:
2156:
2151:
2145:
2143:
2137:
2136:
2134:
2133:
2128:
2127:
2126:
2121:
2111:
2106:
2100:
2098:
2092:
2091:
2089:
2088:
2083:
2078:
2072:
2070:
2069:Summary tables
2066:
2065:
2063:
2062:
2056:
2054:
2048:
2047:
2044:
2043:
2041:
2040:
2039:
2038:
2033:
2028:
2018:
2012:
2010:
2004:
2003:
2001:
2000:
1995:
1990:
1985:
1980:
1975:
1970:
1964:
1962:
1956:
1955:
1953:
1952:
1947:
1942:
1941:
1940:
1935:
1930:
1925:
1920:
1915:
1910:
1905:
1903:Contraharmonic
1900:
1895:
1884:
1882:
1873:
1863:
1862:
1857:
1850:
1849:
1847:
1846:
1841:
1835:
1832:
1831:
1826:
1824:
1823:
1816:
1809:
1801:
1795:
1794:
1763:
1757:
1743:Maddala, G. S.
1739:
1733:
1713:Hayashi, Fumio
1709:
1703:
1676:
1673:
1671:
1670:
1663:
1643:
1624:(3): 497â505.
1602:
1568:
1549:(1): 165â193.
1524:
1503:(3): 289â326.
1487:
1465:
1454:
1435:(2): 251â276.
1410:
1399:(1): 121â130.
1381:
1344:
1323:(2): 111â120.
1302:
1257:
1246:(2): 139â162.
1227:
1225:
1222:
1221:
1220:
1215:
1210:
1203:
1200:
1191:
1188:
1178:
1175:
1156:
1153:
1150:
1147:
1133:
1130:
1118:
1115:
1105:
1102:
1088:
1084:
1080:
1077:
1072:
1068:
1064:
1061:
1056:
1052:
1048:
1028:
1025:
1022:
1000:
996:
971:
967:
963:
958:
955:
952:
948:
944:
941:
938:
933:
929:
925:
922:
917:
913:
909:
887:
884:
881:
874:
871:
845:
841:
837:
815:
811:
807:
784:
762:
758:
735:
731:
708:
704:
679:
649:
645:
624:
599:
595:
583:
582:
568:
564:
560:
555:
551:
547:
544:
539:
535:
509:
505:
484:
455:
451:
428:
424:
405:
402:
397:
394:
379:
376:
373:
370:
320:
317:
314:
311:
286:
283:
280:
277:
253:
250:
247:
244:
203:
200:
181:
178:
175:
172:
146:
143:
57:
50:
43:
26:
24:
18:Co-integration
14:
13:
10:
9:
6:
4:
3:
2:
4150:
4139:
4136:
4134:
4131:
4130:
4128:
4113:
4112:
4103:
4101:
4100:
4091:
4089:
4088:
4083:
4077:
4075:
4074:
4065:
4064:
4061:
4047:
4044:
4042:
4041:Geostatistics
4039:
4037:
4034:
4032:
4029:
4027:
4024:
4023:
4021:
4019:
4015:
4009:
4008:Psychometrics
4006:
4004:
4001:
3999:
3996:
3994:
3991:
3989:
3986:
3984:
3981:
3979:
3976:
3974:
3971:
3969:
3966:
3964:
3961:
3960:
3958:
3956:
3952:
3946:
3943:
3941:
3938:
3936:
3932:
3929:
3927:
3924:
3922:
3919:
3917:
3914:
3913:
3911:
3909:
3905:
3899:
3896:
3894:
3891:
3889:
3885:
3882:
3880:
3877:
3876:
3874:
3872:
3871:Biostatistics
3868:
3864:
3860:
3855:
3851:
3833:
3832:Log-rank test
3830:
3829:
3827:
3823:
3817:
3814:
3813:
3811:
3809:
3805:
3799:
3796:
3794:
3791:
3789:
3786:
3784:
3781:
3780:
3778:
3776:
3772:
3769:
3767:
3763:
3753:
3750:
3748:
3745:
3743:
3740:
3738:
3735:
3733:
3730:
3729:
3727:
3725:
3721:
3715:
3712:
3710:
3707:
3705:
3703:(BoxâJenkins)
3699:
3697:
3694:
3692:
3689:
3685:
3682:
3681:
3680:
3677:
3676:
3674:
3672:
3668:
3662:
3659:
3657:
3656:DurbinâWatson
3654:
3652:
3646:
3644:
3641:
3639:
3638:DickeyâFuller
3636:
3635:
3633:
3629:
3623:
3620:
3618:
3615:
3613:
3612:Cointegration
3610:
3608:
3605:
3603:
3600:
3598:
3595:
3593:
3590:
3588:
3587:Decomposition
3585:
3584:
3582:
3578:
3575:
3573:
3569:
3559:
3556:
3555:
3554:
3551:
3550:
3549:
3546:
3542:
3539:
3538:
3537:
3534:
3532:
3529:
3527:
3524:
3522:
3519:
3517:
3514:
3512:
3509:
3507:
3504:
3502:
3499:
3498:
3496:
3494:
3490:
3484:
3481:
3479:
3476:
3474:
3471:
3469:
3466:
3464:
3461:
3459:
3458:Cohen's kappa
3456:
3455:
3453:
3451:
3447:
3443:
3439:
3435:
3431:
3427:
3422:
3418:
3404:
3401:
3399:
3396:
3394:
3391:
3389:
3386:
3385:
3383:
3381:
3377:
3371:
3367:
3363:
3357:
3355:
3352:
3351:
3349:
3347:
3343:
3337:
3334:
3332:
3329:
3327:
3324:
3322:
3319:
3317:
3314:
3312:
3311:Nonparametric
3309:
3307:
3304:
3303:
3301:
3297:
3291:
3288:
3286:
3283:
3281:
3278:
3276:
3273:
3272:
3270:
3268:
3264:
3258:
3255:
3253:
3250:
3248:
3245:
3243:
3240:
3238:
3235:
3234:
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3207:
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3201:
3199:
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3193:
3189:
3182:
3179:
3177:
3174:
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3169:
3165:
3149:
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3141:
3139:
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3127:
3124:
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3119:
3118:
3117:
3114:
3113:
3111:
3109:
3105:
3095:
3092:
3088:
3082:
3080:
3074:
3072:
3066:
3065:
3064:
3061:
3060:Nonparametric
3058:
3056:
3050:
3046:
3043:
3042:
3041:
3035:
3031:
3030:Sample median
3028:
3027:
3026:
3023:
3022:
3020:
3018:
3014:
3006:
3003:
3001:
2998:
2996:
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2991:
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2975:
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2813:
2809:
2801:
2798:
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2786:
2783:
2781:
2778:
2776:
2773:
2771:
2768:
2766:
2763:
2762:
2760:
2758:
2754:
2748:
2745:
2741:
2738:
2734:
2731:
2729:
2726:
2725:
2724:
2721:
2720:
2719:
2716:
2712:
2709:
2707:
2704:
2702:
2699:
2697:
2694:
2693:
2692:
2689:
2688:
2686:
2684:
2680:
2677:
2675:
2671:
2665:
2662:
2660:
2657:
2653:
2650:
2649:
2648:
2645:
2643:
2640:
2636:
2635:loss function
2633:
2632:
2631:
2628:
2624:
2621:
2619:
2616:
2614:
2611:
2610:
2609:
2606:
2604:
2601:
2599:
2596:
2592:
2589:
2587:
2584:
2582:
2576:
2573:
2572:
2571:
2568:
2564:
2561:
2559:
2556:
2554:
2551:
2550:
2549:
2546:
2542:
2539:
2537:
2534:
2533:
2532:
2529:
2525:
2522:
2521:
2520:
2517:
2513:
2510:
2509:
2508:
2505:
2503:
2500:
2498:
2495:
2493:
2490:
2489:
2487:
2485:
2481:
2477:
2473:
2468:
2464:
2450:
2447:
2445:
2442:
2440:
2437:
2435:
2432:
2431:
2429:
2427:
2423:
2417:
2414:
2412:
2409:
2407:
2404:
2403:
2401:
2397:
2391:
2388:
2386:
2383:
2381:
2378:
2376:
2373:
2371:
2368:
2366:
2363:
2361:
2358:
2357:
2355:
2353:
2349:
2343:
2340:
2338:
2337:Questionnaire
2335:
2333:
2330:
2326:
2323:
2321:
2318:
2317:
2316:
2313:
2312:
2310:
2308:
2304:
2298:
2295:
2293:
2290:
2288:
2285:
2283:
2280:
2278:
2275:
2273:
2270:
2268:
2265:
2263:
2260:
2259:
2257:
2255:
2251:
2247:
2243:
2238:
2234:
2220:
2217:
2215:
2212:
2210:
2207:
2205:
2202:
2200:
2197:
2195:
2192:
2190:
2187:
2185:
2182:
2180:
2177:
2175:
2172:
2170:
2167:
2165:
2164:Control chart
2162:
2160:
2157:
2155:
2152:
2150:
2147:
2146:
2144:
2142:
2138:
2132:
2129:
2125:
2122:
2120:
2117:
2116:
2115:
2112:
2110:
2107:
2105:
2102:
2101:
2099:
2097:
2093:
2087:
2084:
2082:
2079:
2077:
2074:
2073:
2071:
2067:
2061:
2058:
2057:
2055:
2053:
2049:
2037:
2034:
2032:
2029:
2027:
2024:
2023:
2022:
2019:
2017:
2014:
2013:
2011:
2009:
2005:
1999:
1996:
1994:
1991:
1989:
1986:
1984:
1981:
1979:
1976:
1974:
1971:
1969:
1966:
1965:
1963:
1961:
1957:
1951:
1948:
1946:
1943:
1939:
1936:
1934:
1931:
1929:
1926:
1924:
1921:
1919:
1916:
1914:
1911:
1909:
1906:
1904:
1901:
1899:
1896:
1894:
1891:
1890:
1889:
1886:
1885:
1883:
1881:
1877:
1874:
1872:
1868:
1864:
1860:
1855:
1851:
1845:
1842:
1840:
1837:
1836:
1833:
1829:
1822:
1817:
1815:
1810:
1808:
1803:
1802:
1799:
1790:
1786:
1782:
1778:
1777:
1769:
1764:
1760:
1754:
1750:
1749:
1744:
1740:
1736:
1730:
1726:
1721:
1720:
1714:
1710:
1706:
1700:
1696:
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1691:
1685:
1679:
1678:
1674:
1666:
1660:
1656:
1655:
1647:
1644:
1639:
1635:
1631:
1627:
1623:
1619:
1618:
1613:
1606:
1603:
1598:
1594:
1591:(1): 99â126.
1590:
1586:
1579:
1572:
1569:
1564:
1560:
1556:
1552:
1548:
1544:
1543:
1535:
1528:
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1519:
1514:
1510:
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1498:
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1469:
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1463:
1458:
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1450:
1446:
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1411:
1406:
1402:
1398:
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1385:
1382:
1377:
1373:
1369:
1365:
1361:
1357:
1356:
1348:
1345:
1340:
1336:
1331:
1326:
1322:
1318:
1317:
1309:
1307:
1303:
1298:
1294:
1290:
1286:
1282:
1278:
1274:
1270:
1269:
1261:
1258:
1253:
1249:
1245:
1241:
1240:
1232:
1229:
1223:
1219:
1216:
1214:
1211:
1209:
1206:
1205:
1201:
1199:
1197:
1189:
1187:
1185:
1176:
1174:
1172:
1151:
1145:
1131:
1129:
1127:
1123:
1116:
1114:
1111:
1110:Johansen test
1104:Johansen test
1103:
1101:
1086:
1082:
1078:
1075:
1070:
1066:
1059:
1054:
1050:
1026:
1023:
1020:
998:
994:
984:
969:
965:
961:
956:
953:
950:
946:
942:
939:
936:
931:
927:
920:
915:
911:
885:
882:
879:
869:
843:
839:
813:
809:
796:
782:
760:
756:
733:
729:
706:
702:
693:
677:
669:
665:
647:
643:
622:
613:
597:
593:
566:
562:
558:
553:
549:
545:
542:
537:
533:
525:
524:
523:
507:
503:
482:
474:
471:
453:
449:
426:
422:
411:
403:
401:
395:
393:
374:
368:
358:
354:
350:
345:
343:
339:
334:
315:
309:
281:
275:
248:
242:
231:
229:
225:
221:
217:
216:Clive Granger
213:
209:
201:
199:
197:
176:
170:
160:
156:
152:
144:
142:
140:
136:
132:
128:
124:
119:
116: +
115:
112: +
111:
106:
102:
98:
94:
90:
86:
82:
78:
75:. Next, if a
74:
71:
67:
60:
56:
49:
42:
36:
32:
31:Cointegration
19:
4109:
4097:
4078:
4071:
3983:Econometrics
3933: /
3916:Chemometrics
3893:Epidemiology
3886: /
3859:Applications
3701:ARIMA model
3648:Q-statistic
3611:
3597:Stationarity
3493:Multivariate
3436: /
3432: /
3430:Multivariate
3428: /
3368: /
3364: /
3138:Bayes factor
3037:Signed rank
2949:
2923:
2915:
2903:
2598:Completeness
2434:Cohort study
2332:Opinion poll
2267:Missing data
2254:Study design
2209:Scatter plot
2131:Scatter plot
2124:Spearman's Ï
2086:Grouped data
1783:(1): 37â39.
1780:
1774:
1747:
1719:Econometrics
1718:
1689:
1653:
1646:
1621:
1615:
1605:
1588:
1584:
1571:
1546:
1542:Econometrica
1540:
1527:
1500:
1496:
1490:
1478:. Retrieved
1468:
1457:
1432:
1428:Econometrica
1426:
1413:
1396:
1390:
1384:
1362:(1): 64â73.
1359:
1353:
1347:
1320:
1314:
1275:(1): 11â63.
1272:
1266:
1260:
1243:
1237:
1231:
1193:
1180:
1170:
1135:
1126:Sam Ouliaris
1120:
1107:
985:
797:
614:
584:
472:
413:
399:
346:
335:
232:
228:Robert Engle
220:Paul Newbold
205:
148:
145:Introduction
130:
126:
122:
117:
113:
109:
104:
100:
96:
92:
88:
84:
80:
72:
58:
54:
47:
40:
30:
29:
4138:Time series
4111:WikiProject
4026:Cartography
3988:Jurimetrics
3940:Reliability
3671:Time domain
3650:(LjungâBox)
3572:Time-series
3450:Categorical
3434:Time-series
3426:Categorical
3361:(Bernoulli)
3196:Correlation
3176:Correlation
2972:JarqueâBera
2944:Chi-squared
2706:M-estimator
2659:Asymptotics
2603:Sufficiency
2370:Interaction
2282:Replication
2262:Effect size
2219:Violin plot
2199:Radar chart
2179:Forest plot
2169:Correlogram
2119:Kendall's Ï
1518:10983/25617
66:time series
35:statistical
4127:Categories
3978:Demography
3696:ARMA model
3501:Regression
3078:(Friedman)
3039:(Wilcoxon)
2977:Normality
2967:Lilliefors
2914:Student's
2790:Resampling
2664:Robustness
2652:divergence
2642:Efficiency
2580:(monotone)
2575:Likelihood
2492:Population
2325:Stratified
2277:Population
2096:Dependence
2052:Count data
1983:Percentile
1960:Dispersion
1893:Arithmetic
1828:Statistics
1224:References
468:both have
408:See also:
338:unit roots
196:stationary
151:integrated
135:stochastic
107:such that
3359:Logistic
3126:posterior
3052:Rank sum
2800:Jackknife
2795:Bootstrap
2613:Bootstrap
2548:Parameter
2497:Statistic
2292:Statistic
2204:Run chart
2189:Pie chart
2184:Histogram
2174:Fan chart
2149:Bar chart
2031:L-moments
1918:Geometric
1638:153437469
1376:154550363
1325:CiteSeerX
1297:126346450
1083:ε
1063:Δ
1047:Δ
1021:α
966:ε
954:−
943:α
924:Δ
908:Δ
883:−
873:^
836:Δ
806:Δ
783:β
678:β
623:β
546:β
543:−
483:β
349:R-squared
208:Udny Yule
4073:Category
3766:Survival
3643:Johansen
3366:Binomial
3321:Isotonic
2908:(normal)
2553:location
2360:Blocking
2315:Sampling
2194:QâQ plot
2159:Box plot
2141:Graphics
2036:Skewness
2026:Kurtosis
1998:Variance
1928:Heronian
1923:Harmonic
1715:(2000).
1480:4 August
1202:See also
1194:Several
1013:), then
4099:Commons
4046:Kriging
3931:Process
3888:studies
3747:Wavelet
3580:General
2747:Plug-in
2541:L space
2320:Cluster
2021:Moments
1839:Outline
1695:319â386
1563:2938339
1449:1913236
1355:Wilmott
1289:2341482
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268:
264:
235:
202:History
192:
163:
46:,
3968:Census
3558:Normal
3506:Manova
3326:Robust
3076:2-way
3068:1-way
2906:-test
2577:
2154:Biplot
1945:Median
1938:Lehmer
1880:Center
1755:
1731:
1727:â669.
1701:
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1447:
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1295:
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670:. If
585:where
129:, and
3592:Trend
3121:prior
3063:anova
2952:-test
2926:-test
2918:-test
2825:Power
2770:Pivot
2563:shape
2558:scale
2008:Shape
1988:Range
1933:Heinz
1908:Cubic
1844:Index
1771:(PDF)
1634:S2CID
1581:(PDF)
1559:JSTOR
1537:(PDF)
1445:JSTOR
1423:(PDF)
1372:S2CID
1293:S2CID
1285:JSTOR
396:Tests
70:order
33:is a
3825:Test
3025:Sign
2877:Wald
1950:Mode
1888:Mean
1753:ISBN
1729:ISBN
1699:ISBN
1659:ISBN
1482:2014
1360:2012
1124:and
1108:The
495:and
441:and
218:and
3005:BIC
3000:AIC
1785:doi
1725:623
1626:doi
1593:doi
1551:doi
1513:hdl
1505:doi
1437:doi
1401:doi
1364:doi
1335:doi
1277:doi
1248:doi
721:on
666:or
615:If
414:If
353:GNP
64:of
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