Inference for modulated stationary processes

TL;DR

This paper develops self-normalization methods for inference in modulated stationary processes with time-dependent variances, addressing non-stationarity and unknown parameters, and demonstrates their effectiveness through simulations and real data applications.

Contribution

It introduces self-normalization techniques for inference in non-stationary modulated processes, extending existing methods to handle time-dependent variances and large parameter spaces.

Findings

Self-normalized CLT established for modulated processes.

Proposed tests outperform stationary-based methods in simulations.

Method successfully applied to climate and economic data.

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.