Dating multiple change points in the correlation matrix
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A nonparametric procedure for detecting and dating multiple change points in the correlation matrix of sequences of random variables is proposed. The procedure is based on a recently proposed test for changes in correlation matrices at an unknown point in time. Although the procedure requires constant expectations and variances, only mild assumptions on the serial dependence structure are assumed. The convergence rate of the change point estimators is derived and the asymptotic validity of the procedure is proved. Moreover, the performance of the proposed algorithm in finite samples is illustrated by means of a simulation study and the analysis of a real data example with financial returns. These examples show that the algorithm has large power in finite samples.
KeywordsBinary segmentation algorithm Correlation matrix CUSUM statistics Financial returns Multiple change point detection Nonparametric estimation
Mathematics Subject Classification62M10 62G10 91B84
Financial support by Ministerio de Economía y Competitividad Grant ECO2015-66593-P and Deutsche Forschungsgemeinschaft (SFB 823, project A1) is gratefully acknowledged. We also would like to thank three anonymous referees for very helpful comments.
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