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

Yuriy Kozachenko,Viktor Troshki

doi:10.15559/15-vmsta17

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.

Highlights

We construct a criterion for testing the hypothesis that the covariance function of measurable real-valued stationary Gaussian stochastic process X(t) equals ρ(τ )
The main properties of the correlograms of stationary Gaussian stochastic processes were studied by Buldygin and Kozachenko [3]
In the papers [5] and [8], Kozachenko and Fedoryanich constructed a criterion for testing hypotheses about the covariance function of a Gaussian stationary process with given accuracy and reliability in L2(T)

Summary

Introduction

We construct a criterion for testing the hypothesis that the covariance function of measurable real-valued stationary Gaussian stochastic process X(t) equals ρ(τ ). In the papers [5] and [8], Kozachenko and Fedoryanich constructed a criterion for testing hypotheses about the covariance function of a Gaussian stationary process with given accuracy and reliability in L2(T). We obtain the estimate for the norm of square Gaussian stochastic processes in the space Lp(T). We use this estimate for constructing a criterion for testing hypotheses about the covariance function of a Gaussian stochastic process.

Some information about the square Gaussian random variables and processes

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