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.
Citation
Zhibiao Zhao. Xiaoye Li. "Inference for modulated stationary processes." Bernoulli 19 (1) 205 - 227, February 2013. https://doi.org/10.3150/11-BEJ399
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