A criterion for testing hypotheses about the covariance function of a stationary Gaussian stochastic process

TL;DR

This paper develops a statistical criterion for testing hypotheses about the covariance function of a stationary Gaussian process, utilizing estimates of its norm in the $L_p$ space for $p \,\geq\,1$, aiding in hypothesis validation.

Contribution

The paper introduces a new criterion based on $L_p$ norm estimates for testing covariance hypotheses in stationary Gaussian processes, advancing existing statistical testing methods.

Findings

Provides a measurable criterion for hypothesis testing

Utilizes $L_p$ norm estimates for covariance functions

Applicable to stationary Gaussian processes

Abstract

We consider a measurable stationary Gaussian stochastic process. A criterion for testing hypotheses about the covariance function of such a process using estimates for its norm in the space $L_p(\mathbb {T}),\,p\geq1$, is constructed.