Detecting Variance Change-Points for Blocked Time Series and Dependent Panel Data

This article proposes a class of weighted differences of averages (WDA) statistics to test and estimate possible change-points in variance for time series with weakly dependent blocks and dependent panel data without specific distributional assumptions. We derive the asymptotic distributions of the test statistics for testing the existence of a single variance change-point under the null and local alternatives. We also study the consistency of the change-point estimator. Within the proposed class of the WDA test statistics, a standardized WDA test is shown to have the best consistency rate and is recommended for practical use. An iterative binary searching procedure is suggested for estimating the locations of possible multiple change-points in variance, whose consistency is also established. Simulation studies are conducted to compare detection power and number of wrong rejections of the proposed procedure to that of a cumulative sum (CUSUM) based test and a likelihood ratio-based test. Finally, we apply the proposed method to a stock index dataset and an unemployment rate dataset. Supplementary materials for this article are available online.NSF [DMS-1309156, DMS-1209112]; National Natural Science Foundation of China [10901010]; Key Program of National Natural Science Foundation of China [11131002]; Center for Statistical Science in Peking University; Key Laboratory of Mathematical Economics and Quantitative Finance (Peking University), Ministry of EducationSCI(E)SSCIARTICLEminyaxu@gsm.pku.edu.cn; pszhong@stt.msu.edu; weiwang@galton.uchicago.edu2213-2263