A spectral approach to estimate the autocovariance function

Abstract

This paper proposes two novel alternative estimators for the autocovariance function of a short-range dependent stationary process based on a spectral approach. One is based on the classical periodogram, and the other one uses the M-periodogram. The theoretical properties of both estimators are investigated for linear processes. Monte-Carlo experiments are conducted to compare these estimators to the standard sample autocovariance function in autoregressive moving average (ARMA) models with and without additive outliers. In the non-contaminated scenario, the empirical investigation shows that the three estimators display similar performance. However, in the contaminated case, the estimator based on the M-periodogram remains unaffected in the presence of additive outliers, while the two other estimators are corrupted.