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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.
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https://hal-centralesupelec.archives-ouvertes.fr/hal-03695445
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Submitted on : Tuesday, June 14, 2022 - 5:49:01 PM
Last modification on : Saturday, June 25, 2022 - 3:26:38 AM

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

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