Quantile tests in frequency domain for sinusoid models

TL;DR

This paper introduces quantile-based tests in the frequency domain for stationary processes, proposing estimators, analyzing their properties, and demonstrating their effectiveness through numerical studies.

Contribution

It develops new frequency domain quantile estimators for spectral distribution functions and provides a testing procedure with proven asymptotic properties.

Findings

Strong statistical power demonstrated in numerical simulations

Asymptotic properties of the estimators established

Difference from time domain quantile estimators discussed

Abstract

For second order stationary processes, the spectral distribution function is uniquely deter- mined by the autocovariance functions of the processes. We define the quantiles of the spectral distribution function and propose two estimators for the quantiles. Asymptotic properties of both estimators are elucidated and the difference from the quantile estimators in time do- main is also indicated. We construct a testing procedure of quantile tests from the asymptotic distribution of the estimators and strong statistical power is shown in our numerical studies.