Inference for modulated stationary processes

• Published in: Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability Vol. 19; no. 1; p. 205
• Main Authors: Zhao, Zhibiao, Li, Xiaoye
• Format: Journal Article
• Language: English
• Published: England 01.02.2013
• Subjects: Wild bootstrap; Change-point analysis; Modulated stationary process; Self-normalization; Strong invariance principle; Long-run variance; Confidence interval
• ISSN: 1350-7265
• DOI: 10.3150/11-BEJ399

We study statistical inferences for a class of modulated stationary processes with time-dependent variances. Due to non-stationarity and the large number of unknown parameters, existing methods for stationary or locally stationary time series are not applicable. Based on a self-normalization technique, we address several inference problems, including self-normalized central limit theorem, self-normalized cumulative sum test for the change-point problem, long-run variance estimation through blockwise self-normalization, and self-normalization-based wild boot-strap. Monte Carlo simulation studies show that the proposed self-normalization-based methods outperform stationarity-based alternatives. We demonstrate the proposed methodology using two real data sets: annual mean precipitation rates in Seoul during 1771-2000, and quarterly U.S. Gross National Product growth rates during 1947-2002.