title: Inference for modulated stationary processes.
abstract: 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.
authors.affiliation: Department of Statistics, Penn State University, University Park, PA 16802.
authors.forename: Zhibiao
authors.initials: Z
authors.lastname: Zhao
authors.forename: Xiaoye
authors.initials: X
authors.lastname: Li
keywords: Change-point analysis; Confidence interval; Long-run variance; Modulated stationary process; Self-normalization; Strong invariance principle; Wild bootstrap
references.citation: Biometrika. 2011;98(1):
references.pmid: 24319293