LARGE DEVIATION PRINCIPLE FOR THE SAMPLE COVARIANCE FUNCTION OF A FIRST ORDER AUTOREGRESSIVE PROCESS

Abstract

This paper describes a large deviation principle for the sample covariance function ⁿΣ_i=1X_iX_i-1/n of a first order non-explosive Gaussian autoregressive process with unknown autoregressive parameter θ, the rate function is also provided. The asymptotic rate of convergence of the tail probability of the sample covariance function is also studied.