Block bootstrapping for a panel mean break test
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Online ISSN 2005-2863 Print ISSN 1226-3192
RESEARCH ARTICLE
Block bootstrapping for a panel mean break test Ji-Eun Choi1 · Dong Wan Shin1 Received: 23 June 2019 / Accepted: 4 November 2019 © Korean Statistical Society 2020
Abstract We consider block bootstrappings for panel mean change test of the squared CUSUM test of Horváth and Hušková (J Time Ser Anal 33:631–648, 2012): the circular block bootstrapping and stationary bootstrapping. First order asymptotic null validity of the test is proved under serial and/or cross-sectional correlation. Consistency of the test under an alternative hypothesis is also proved. A Monte-Carlo experiment reveals that the existing tests of Horváth and Hušková (2012) and others have severe size distortions for serially and/or cross-sectionally correlated panels, and the block bootstrappings remedy this size distortion problem. A real data analysis illustrates the proposed method. Keywords Bootstrap test · Panel mean break · Cross-sectional dependence · Serial dependence · Circular block bootstrapping · Stationary bootstrapping Mathematics Subject Classification 62H15 · 62F40
1 Introduction Structural changes for mean level frequently occur in financial or economic time series. Since the mean change yields inconsistent estimator and brings several problems in forecasting and in analyzing causality, mean change detection has been an important issue in many studies, see Bai et al. (1998), Hansen (2000), Geweke and Jiang (2011) and many others. However, causative factors of the mean changes, such as change in macroeconomic policy, international situation and finance crisis have simultaneous influences on countries or companies. Therefore, structural change detection problem has been also discussed in a panel context which can address the simultaneous influences: Bai et al. (1998) for multivariate time series with stationary, non-stationary and trendy
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Dong Wan Shin [email protected] Department of Statistics, Ewha University, Seoul, Korea
123
Journal of the Korean Statistical Society
processes, Qu and Perron (2007) for multivariate regressions and Bai (2010) for independent panels. In particular, Bai (2010) was adopted by recent panel mean break studies. See Horváth and Hušková (2012), Kim (2011, 2014), Li et al. (2016) . On the other hand, Demetrescu and Hanck (2013) studied a panel unit root test under structural breaks in the error variance. Among these papers, the common mean break detection test of Horváth and Hušková (2012) was constructed by applying the quasi-maximum likelihood method based on the squared CUSUM of Bai (2010). The break test showed a good power performance in independent panels against both non-canceling breaks and canceling breaks and is widely accepted in the literature. However, as will be shown in Sect. 4, the test of Horváth and Hušková (2012) has undesirable size distortion under serial and/or cross-sectional dependence, which are main features of financial or economic panel data sets. Sharipov et al. (2016) constructed a break test in a Hibert sp
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