Open Access
February 2013 Inference for modulated stationary processes
Zhibiao Zhao, Xiaoye Li
Bernoulli 19(1): 205-227 (February 2013). 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 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.


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Zhibiao Zhao. Xiaoye Li. "Inference for modulated stationary processes." Bernoulli 19 (1) 205 - 227, February 2013.


Published: February 2013
First available in Project Euclid: 18 January 2013

zbMATH: 1259.62077
MathSciNet: MR3019492
Digital Object Identifier: 10.3150/11-BEJ399

Keywords: change-point analysis , Confidence interval , long-run variance , modulated stationary process , self-normalization , Strong invariance principle , wild bootstrap

Rights: Copyright © 2013 Bernoulli Society for Mathematical Statistics and Probability

Vol.19 • No. 1 • February 2013
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