Kybernetika 54 no. 6, 1106-1121, 2018

Structural breaks in dependent, heteroscedastic, and extremal panel data

Matúš Maciak, Barbora Peštová and Michal PeštaDOI: 10.14736/kyb-2018-6-1106

Abstract:

New statistical procedures for a~change in means problem within a~very general panel data structure are proposed. Unlike classical inference tools used for the changepoint problem in the panel data framework, we allow for mutually dependent panels, unequal variances across the panels, and possibly an~extremely short follow up period. Two competitive ratio type test statistics are introduced and their asymptotic properties are derived for a~large number of available panels. The proposed tests are proved to be consistent and their empirical properties are investigated in an~extensive simulation study. The suggested testing approaches are also applied to a~real data problem.

Keywords:

consistency, panel data, dependence within panels, dependence between panels, changepoint, short panels, heteroscedasticity, ratio type statistics

Classification:

62H15, 62H10, 62E20, 62P05, 62F40

paper.pdf

References:

  1. J. Bai: Common breaks in means and variances for panel data. J. Econometrics 157 (2010), 78-92.   DOI:10.1016/j.jeconom.2009.10.020
  2. B. H. Baltagi, Q. Feng and C. Kao: Estimation of heterogeneous panels with structural breaks. J. Econometrics 191 (2016), 176-195.   DOI:10.1016/j.jeconom.2015.03.048
  3. P. Billingsley: Probability and Measure. Second edition. John Wiley and Sons, New York 1986.   CrossRef
  4. J. Chan, L. Horváth and M. Hušková: Change-point detection in panel data. J. Statist. Plann. Inference 143 (2013), 955-970.   DOI:10.1016/j.jspi.2012.11.004
  5. Z. Chen and Z. Tian: Ratio tests for variance change in nonparametric regression. Statistics 48 (2014), 1-16.   DOI:10.1080/02331888.2012.708030
  6. M. Csörgő and L. Horváth: Limit Theorems in Change-Point Analysis. Wiley Publisher, Chichester 1997.   CrossRef
  7. L. Horváth, Z. Horváth and M. Hušková: Ratio tests for change point detection. In: Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of Professor Pranab K. Sen (N. Balakrishnan, E. A. Peña, and M. J. Silvapulle, eds.), IMS Collections, Beachwood 2009, pp. 293-304.   DOI:10.1214/193940307000000220
  8. L. Horváth and M. Hušková: Change-point detection in panel data. J. Time Series Anal. 33 (2012), 631-648.   DOI:10.1111/j.1467-9892.2012.00796.x
  9. D. Kim: Estimating a common deterministic time trend break in large panels with cross section dependence. J. Econometrics 164 (2011), 310-330.   DOI:10.1016/j.jeconom.2011.06.018
  10. A. M. Lindner: Stationarity, mixing, distributional properties and moments of {GARCH(p,q)}-processes. In: Handbook of Financial Time Series (T. G. Andersen., R. A. Davis, J. P. Kreiss, and T. Mikosch, eds.), Springer, Berlin 2009, pp. 481-496.   DOI:10.1007/978-3-540-71297-8\_2
  11. Y. Liu, C. Zou and R. Zhang: Empirical likelihood ratio test for a change-point in linear regression model. Comm. Statist. Theory Methods 37 (2008), 2551-2563.   DOI:10.1080/03610920802040373
  12. B. Madurkayová: Ratio type statistics for detection of changes in mean. Acta Universitatis Carolinae: Mathematica et Physicas 52 (2011), 47-58.   CrossRef
  13. G. G. Meyers and P. Shi: Loss Reserving Data Pulled from NAIC Schedule P.    CrossRef
  14. M. Pesaran: Estimation and inference in large heterogeneous panels with a multifactor error structure. Econometrica 74 (2006), 967-1012.   DOI:10.1111/j.1468-0262.2006.00692.x
  15. M. Pešta and Š. Hudecová: Asymptotic consistency and inconsistency of the chain ladder. Insurance Math. Econom. 51 (2012), 472-479.   DOI:10.1016/j.insmatheco.2012.07.004
  16. B. Peštová and M. Pešta: Testing structural changes in panel data with small fixed panel size and bootstrap. Metrika 78 (2015), 665-689.   DOI:10.1007/s00184-014-0522-8
  17. B. Peštová and M. Pešta: Change point estimation in panel data without boundary issue. Risks 5 (2017), 7.   DOI:10.3390/risks5010007
  18. J. Qian and L. Su: Shrinkage estimation of regression models with multiple structural changes. Econometr. Theory 32 (2016), 1376-1433.   DOI:10.1017/s0266466615000237
  19. S. De Watcher and E. Tzavalis: Detection of structural breaks in linear dynamic panel data models. Comput. Statist. Data Anal. 56 (2012), 3020-3034.   DOI:10.1016/j.csda.2012.02.025