On maxima of periodograms of stationary processes

TL;DR

This paper investigates the asymptotic behavior of the maximum values of periodograms derived from stationary processes, utilizing m-dependent approximation techniques and moderate deviation results to establish their limit distribution.

Contribution

It introduces a novel approach combining m-dependent approximation and moderate deviations to analyze the maxima of periodograms for stationary processes.

Findings

Derived the limit distribution of periodogram maxima.

Established the effectiveness of m-dependent approximation.

Provided theoretical insights into spectral analysis of stationary processes.

Abstract

We consider the limit distribution of maxima of periodograms for stationary processes. Our method is based on $m$-dependent approximation for stationary processes and a moderate deviation result.