Change Point in Panel Data with Small Fixed Panel Size: Ratio and Non-ratio Test Statistics

  • Barbora Peštová
  • Michal Pešta
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 231)


The main goal is to develop and, consequently, compare stochastic methods for detecting whether a structural change in panel data occurred at some unknown time or not. Panel data of our interest consist of a moderate or relatively large number of panels, while the panels contain a small number of observations. Testing procedures to detect a possible common change in means of the panels are established. Ratio and non-ratio type test statistics are considered. Their asymptotic distributions under the no change null hypothesis are derived. Moreover, we prove the consistency of the tests under the alternative. The advantage of the ratio statistics compared to the non-ratio ones is that the variance of the observations neither has to be known nor estimated. A simulation study reveals that the proposed ratio statistic outperforms the non-ratio one by keeping the significance level under the null, mainly when stronger dependence within the panel is present. However, the non-ratio statistic incorrectly rejects the null in the simulations more often than it should, which yields higher power compared to the ratio statistic.


Change point Panel data Change in mean Hypothesis testing Structural change Ratio type statistics 



The authors would like to thank an anonymous referee for the suggestions that improved this chapter. Institutional support to Barbora Peštová was provided by RVO:67985807. The research of Michal Pešta was supported by the Czech Science Foundation project “DYME—Dynamic Models in Economics” No. P402/12/G097.


  1. 1.
    Andrews, D.W.K.: Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica 59(3), 817–858 (1991)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bai, J.: Common breaks in means and variances for panel data. J. Econom. 157(1), 78–92 (2010)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Bai, J., Carrion-I-Silvestre, J.L.: Structural changes, common stochastic trends, and unit roots in panel data. Rev. Econ. Stud. 76(2), 471–501 (2009)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Chan, J., Horváth, L., Hušková, M.: Change-point detection in panel data. J. Stat. Plan. Infer. 143(5), 955–970 (2013)CrossRefGoogle Scholar
  5. 5.
    Csörgő, M., Horváth, L.: Limit Theorems in Change-Point Analysis. Wiley, Chichester (1997)zbMATHGoogle Scholar
  6. 6.
    Horváth, L., Horváth, Z., Hušková, M.: Ratio tests for change point detection. In: Balakrishnan, N., Peña, E.A., Silvapulle, M.J. (eds.) Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of Professor Pranab K. Sen, vol. 1, pp. 293–304. IMS Collections, Beachwood, Ohio (2009)Google Scholar
  7. 7.
    Horváth, L., Hušková, M.: Change-point detection in panel data. J. Time Ser. Anal. 33(4), 631–648 (2012)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Im, K.S., Lee, J., Tieslau, M.: Panel LM unit-root tests with level shifts. Oxford B. Econ. Stat. 67(3), 393–419 (2005)CrossRefGoogle Scholar
  9. 9.
    Lindner, A.M.: Stationarity, mixing, distributional properties and moments of GARCH(p, q)-processes. In: Andersen, T.G., Davis, R.A., Kreiss, J.P., Mikosch, T. (eds.) Handbook of Financial Time Series, pp. 481–496. Springer, Berlin (2009)CrossRefGoogle Scholar
  10. 10.
    Madurkayová, B.: Ratio type statistics for detection of changes in mean. Acta Universitatis Carolinae: Mathematica et Physica 52(1), 47–58 (2011)MathSciNetzbMATHGoogle Scholar
  11. 11.
    Peštová, B., Pešta, M.: Testing structural changes in panel data with small fixed panel size and bootstrap. Metrika 78(6), 665–689 (2015)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Peštová, B., Pešta, M.: Erratum to: Testing structural changes in panel data with small fixed panel size and bootstrap. Metrika 79(2), 237–238 (2016)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Medical Informatics and BiostatisticsInstitute of Computer Science, The Czech Academy of SciencesPragueCzech Republic
  2. 2.Faculty of Mathematics and Physics, Department of Probability and Mathematical StatisticsCharles UniversityPragueCzech Republic

Personalised recommendations