A spectral approach to estimate the autocovariance function

Céline Lévy-Leduc (1) , Pascal Bondon (2) , Valdério Reisen (3)

1 MIA Paris-Saclay - Mathématiques et Informatique Appliquées
2 L2S - Laboratoire des signaux et systèmes
3 UFES - Universidade Federal do Espirito Santo

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.

Keywords: Autocovariance function; additive outliers; M-periodogram

Domains: Statistics Theory [stat.TH]

Céline Lévy-Leduc, Pascal Bondon, Valdério Reisen. A spectral approach to estimate the autocovariance function. Journal of Statistical Planning and Inference, 2022, 221, pp.281-298. ⟨10.1016/j.jspi.2022.05.005⟩. ⟨hal-03695445⟩