Optimal Difference-Based Variance Change Point Detection on Mean-Nonstationary Time Series

• Activity Number: 89 - Nonparametric Methods for Modern Data
• Type: Contributed
• Date/Time: Monday, August 9, 2021 : 10:00 AM to 11:50 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Kin Wai Chan and Cheuk Wai Dominic Leung*
• Companies: The Chinese University of Hong Kong and The Chinese University of Hong Kong
• Keywords: CUSUM; Variance change point; Variate difference method; Time series

Abstract

Traditional Cumulative Sum (CUSUM) tests for a variance change point are vulnerable to the masking of a smoothly-varying mean structure, as mean constancy is usually assumed in those traditional methods. In this talk, we use a Double Step Difference Sequence (DS^2) to circumvent the problem. We propose a general and optimal framework to transform the original time series by a differencing technique, so that it is robust to the varying mean structure and is also optimal with respect to the serial dependence structure. The DS^2 method further streamlines the differencing technique, to perform robust pilot estimation in order to obtain the empirical optimal difference sequence. Simulation result shows a substantial improvement in test power over traditional methods.