Inference for modulated stationary processes

Zhibiao Zhao, Xiaoye Li

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

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 a self-normalized central limit theorem, a self-normalized cumulative sum test for the change-point problem, a long-run variance estimation through blockwise self-normalization, and a self-normalization-based wild bootstrap. 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 from 1771-2000, and quarterly U.S. Gross National Product growth rates from 1947-2002.

Original languageEnglish (US)
Pages (from-to)205-227
Number of pages23
JournalBernoulli
Volume19
Issue number1
DOIs
StatePublished - Feb 2013

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

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