Confidence estimation of the covariance function of stationary and locally stationary processes

Summury In this note we consider the problem of confidence estimation of the covariance function of a stationary or locally stationary zero mean Gaussian process. The constructed confidence intervals are based on the usual empirical covariance estimate and a special estimate of its variance. The results about coverage probability are stated in a nonasymptotic way and apply for small and moderate sample size under mild conditions on the model. The presented numerical results are in agreement with the theoretical issues and demonstrate applicability of the method.