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Testing for Parameter Constancy in Linear Regressions: An Empirical Distribution Function Approach

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  • Bai, Jushan

Abstract

This paper proposes some tests for parameter constancy in linear regressions. The tests use weighted empirical distribution functions of estimated residuals and are asymptotically distribution free. The proposed tests have nontrivial local power against a wide range of alternatives. In particular, the tests are capable of detecting error heterogeneity that is not necessarily manifested in the form of changing variances. The model allows for both dynamic and trending regressors. As an intermediate result, some weak convergence for (stochastically) weighted sequential empirical processes is established. Copyright 1996 by The Econometric Society.

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  • Bai, Jushan, 1996. "Testing for Parameter Constancy in Linear Regressions: An Empirical Distribution Function Approach," Econometrica, Econometric Society, vol. 64(3), pages 597-622, May.
  • Handle: RePEc:ecm:emetrp:v:64:y:1996:i:3:p:597-622
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    Cited by:

    1. Caner,M. & Hansen,B.E., 1998. "Threshold autoregression with a near unit root," Working papers 27, Wisconsin Madison - Social Systems.
    2. Gebrenegus Ghilagaber, 2004. "Another Look at Chow's Test for the Equality of Two Heteroscedastic Regression Models," Quality & Quantity: International Journal of Methodology, Springer, vol. 38(1), pages 81-93, February.
    3. repec:eee:csdana:v:116:y:2017:i:c:p:49-66 is not listed on IDEAS
    4. Chandra, S. Ajay, 2009. "Testing the equality of error distributions from k independent GARCH models," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1245-1260, July.
    5. repec:bla:jtsera:v:38:y:2017:i:1:p:99-119 is not listed on IDEAS
    6. Bai, Jushan & Ng, Serena, 2001. "A consistent test for conditional symmetry in time series models," Journal of Econometrics, Elsevier, vol. 103(1-2), pages 225-258, July.
    7. Delgado, Miguel A. & Stute, Winfried, 2008. "Distribution-free specification tests of conditional models," Journal of Econometrics, Elsevier, vol. 143(1), pages 37-55, March.
    8. Han, Heejoon & Linton, Oliver & Oka, Tatsushi & Whang, Yoon-Jae, 2016. "The cross-quantilogram: Measuring quantile dependence and testing directional predictability between time series," Journal of Econometrics, Elsevier, vol. 193(1), pages 251-270.
    9. Hiroyuki Kawakatsu & Matthew R. Morey, 1999. "An Empirical Examination Of Financial Liberalization And The Efficiency Of Emerging Market Stock Prices," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 22(4), pages 385-411, December.
    10. Oka, Tatsushi & Qu, Zhongjun, 2011. "Estimating structural changes in regression quantiles," Journal of Econometrics, Elsevier, vol. 162(2), pages 248-267, June.
    11. Venkata Jandhyala & Stergios Fotopoulos & Ian MacNeill & Pengyu Liu, 2013. "Inference for single and multiple change-points in time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(4), pages 423-446, July.
    12. Hinich, Melvin J. & Foster, John & Wild, Phillip, 2006. "Structural change in macroeconomic time series: A complex systems perspective," Journal of Macroeconomics, Elsevier, vol. 28(1), pages 136-150, March.
    13. Cho, Jin Seo & White, Halbert, 2011. "Generalized runs tests for the IID hypothesis," Journal of Econometrics, Elsevier, vol. 162(2), pages 326-344, June.
    14. Qu, Zhongjun & Yoon, Jungmo, 2015. "Nonparametric estimation and inference on conditional quantile processes," Journal of Econometrics, Elsevier, vol. 185(1), pages 1-19.
    15. Juhl, Ted & Xiao, Zhijie, 2005. "A nonparametric test for changing trends," Journal of Econometrics, Elsevier, vol. 127(2), pages 179-199, August.
    16. Shinn-Juh Lin & Jian Yang, 2000. "Testing Shifts in Financial Models with Conditional Heteroskedasticity: An Empirical Distribution Function Approach," Econometric Society World Congress 2000 Contributed Papers 0063, Econometric Society.
    17. Su, Liangjun & Xiao, Zhijie, 2008. "Testing for parameter stability in quantile regression models," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2768-2775, November.
    18. Jamie Emerson & Chihwa Kao, 2000. "Testing for Structural Change of a Time Trend Regression in Panel Data," Center for Policy Research Working Papers 15, Center for Policy Research, Maxwell School, Syracuse University.
    19. Delgado, Miguel A. & Farinas, Jose C. & Ruano, Sonia, 2002. "Firm productivity and export markets: a non-parametric approach," Journal of International Economics, Elsevier, vol. 57(2), pages 397-422, August.
    20. Zhou, Mi & Wang, Huixia Judy & Tang, Yanlin, 2015. "Sequential change point detection in linear quantile regression models," Statistics & Probability Letters, Elsevier, vol. 100(C), pages 98-103.
    21. Kuan, Chung-Ming, 1998. "Tests for changes in models with a polynomial trend," Journal of Econometrics, Elsevier, vol. 84(1), pages 75-91, May.
    22. Mehmet Caner & Bruce E. Hansen, 2001. "Threshold Autoregression with a Unit Root," Econometrica, Econometric Society, vol. 69(6), pages 1555-1596, November.
    23. Yang, Jian, 2001. "Structural change tests under regression misspecifications," Economics Letters, Elsevier, vol. 70(3), pages 311-317, March.
    24. Li, Dong & Li, Qi, 2010. "Nonparametric/semiparametric estimation and testing of econometric models with data dependent smoothing parameters," Journal of Econometrics, Elsevier, vol. 157(1), pages 179-190, July.

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