Bernoulli

  • Bernoulli
  • Volume 19, Number 1 (2013), 205-227.

Inference for modulated stationary processes

Zhibiao Zhao and Xiaoye Li

Full-text: Open access

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.

Article information

Source
Bernoulli, Volume 19, Number 1 (2013), 205-227.

Dates
First available in Project Euclid: 18 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.bj/1358531747

Digital Object Identifier
doi:10.3150/11-BEJ399

Mathematical Reviews number (MathSciNet)
MR3019492

Zentralblatt MATH identifier
1259.62077

Keywords
change-point analysis confidence interval long-run variance modulated stationary process self-normalization strong invariance principle wild bootstrap

Citation

Zhao, Zhibiao; Li, Xiaoye. Inference for modulated stationary processes. Bernoulli 19 (2013), no. 1, 205--227. doi:10.3150/11-BEJ399. https://projecteuclid.org/euclid.bj/1358531747


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