Abstract
Stationary bootstrapping is applied to a CUSUM test for common mean break detection in cross-sectionally correlated panel data. Asymptotic null distribution of the bootstrapped test is derived, which is the same as that of the original CUSUM test depending on cross-sectional correlation parameter. A bootstrap test using the CUSUM test with bootstrap critical values is proposed and its asymptotic validity is proved. Finite sample Monte-Carlo simulation shows that the proposed test has reasonable size while other existing tests have severe size distortion under cross-section correlation. The simulation also shows good power performance of the proposed test against non-cancelling mean changes. The simulation also shows that the theoretically justified stationary bootstrapping CUSUM test has comparable size and power relative to other, theoretically unjustified, moving block or tapered block bootstrapping CUSUM tests.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Andrews DWK (1991) Heteroscedasticity and autocorrelation consistent covariance matrix estimation. Econometrica 59:817–854
Aue A, Horvath L (2013) Structural breaks in time series. J Time Ser Anal 34:1–16
Bai J (2010) Common breaks in means and variances for panel data. J Econom 157:78–92
Bai J, Ng S (2004) A PANIC attack on unit roots and cointegration. Econometrica 71:135–171
Becheri IG, Drost FC, Akker R (2015) Unit root tests for cross-sectionally dependent panels: the influence of observed factors. J Stat Plan Inference 160:11–22
Billingsley P (1999) Convergence of probability measures, 2nd edn. Wiley, New York
Chang Y (2004) Bootstrap unit root tests in panels with cross-sectional dependency. J Econom 120:263–293
Hall P, Heyde CC (1980) Martingale limit theory and its application. Academic Press, New York
Herrndorf N (1984) A functional central limit theorem for weakly dependent sequences of random variables. Ann Prob 12:141–153
Horvath L, Huskova M (2012) Change-point detection in panel data. J Time Ser Anal 33:631–648
Huang X (2013) Nonparametric estimation in large panels with cross-sectional dependecne. Econom Rev 32:754–777
Hwang E, Shin DW (2015) Stationary bootstrapping for semiparametric panel unit root tests. Comput Stat Data Anal 83:14–25
Hwang E, Shin DW (2016) Maximal inequalities and an application under a weak dependence. J Korean Math Soc 53:57–72
Kapetanios G, Mitchell J, Shin Y (2014) A nonlinear panel data model of cross-sectional dependence. J Econom 179:134–157
Kim D (2014) Common breaks in time trends for large panel data with a factor structure. Econom J 17:301–337
Kunsch H (1989) The jackknife and the bootstrap for general stationary observations. Ann Stat 17:1217–41
Li F, Tian Z, Xiao Y, Chen Z (2015) Variance change-point detection in panel data models. Econ Lett 126:140–143
Meligkotsidou L, Tzavalis E, Vrontos ID (2014) A Bayesian method of distinguishing unit root from stationary processes based on panel data medels with cross-sectional dependence. Stat Comput 24:297–315
Moon HR, Perron B (2004) Testing for a unit root in panels with dynamic factors. J Econom 122:81–126
Paparoditis E, Politis DN (2001) Tapered block bootstrap. Biometrika 88:1105–1119
Paparoditis E, Politis D (2005) Bootstrapping unit root tests for autoregressive time series. J Am Stat Assoc 100:545–553
Parker C, Paparoditis E, Politis DN (2006) Unit root testing via the stationary bootstrap. J Econom 133:601–638
Phillips PCB, Solo V (1992) Asymptotics for linear processes. Ann Stat 20:971–1001
Phillips PCB, Sul D (2003) Dynamic panel estimation and homogeneity testing under cross section dependence. Econom J 6:217–259
Politis DN, Romano JP (1994) The stationary bootstrap. J Am Stat Assoc 89:1303–1313
Politis DN, White H (2004) Automatic block-length selection for the dependent bootstrap. Econom Rev 23:53–70
Shi Y (2015) Testing change in volatility using panel data. Econ Lett 134:107–110
Shin DW (2015) Stationary bootstrapping for panel cointegration tests under cross-sectional dependence. Statistics 49:209–223
Shin DW, Kang S (2006) An instrumental variable approach for panel unit root tests under cross-sectional dependence. J Econom 134:215–234
Shin DW, Hwang E (2013) Stationary bootstrapping for cointegrating regressions. Stat Prob Lett 83:474–480
Shin DW, Hwang E (2017) A CUSUM test for panel mean change detection. J Korean Stat Soc 46:70–77
Swensen AR (2003) Bootstrapping unit root tests for integrated processes. J Time Ser Anal 24:99–126
Yang SC (2007) Maximal moment inequalty for partial sums of strong mixing sequences and applications. Acta Math Sin English Ser 23:1013–1024
Acknowledgements
The authors are very grateful for the constructive comments of a referee which lead us to a substantially improved paper. This study was supported by grants from the National Research Foundation of Korea (NRF-2016R1A2B4008780, NRF-2015-1006133).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Hwang, E., Shin, D.W. Stationary bootstrapping for common mean change detection in cross-sectionally dependent panels. Metrika 80, 767–787 (2017). https://doi.org/10.1007/s00184-017-0627-y
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00184-017-0627-y