Wasserstein distance bounds on the normal approximation of empirical autocovariances and cross‐covariances under non‐stationarity and stationarity

Artikel

The autocovariance and cross-covariance functions naturally appear in many time series procedures (e.g. autoregression or prediction). Under assumptions, empirical versions of the autocovariance and cross-covariance are asymptotically normal with covariance structure depending on the second- and fourth-order spectra. Under non-restrictive assumptions, we derive a bound for the Wasserstein distance of the finite-sample distribution of the estimator of the autocovariance and cross-covariance to the Gaussian limit. An error of approximation to the second-order moments of the estimator and an m-dependent approximation are the key ingredients to obtain the bound. As a worked example, we discuss how to compute the bound for causal autoregressive processes of order 1 with different distributions for the innovations. To assess our result, we compare our bound to Wasserstein distances obtained via simulation.

Angaben zum Objekt

• Sprache: Englisch

Verweise und Beziehungen

• Erschienen in: Journal: Journal of Time Series Analysis ; ISSN: 1467-9892 ; Volume: 45 ; Year: 2023 ; Issue: 3 ; Pages: 361-375 ; Hoboken, NJ: Wiley

Klassifikation und Themen

• Thema: Autocovariance ; time series ; Wasserstein distance ; Stein's method

Beteiligte, Orts- und Zeitangaben

• Ereignis: Geistige Schöpfung
• (wer): Anastasiou, Andreas ; Kley, Tobias
• Ereignis: Veröffentlichung
• (wer): Wiley
• (wo): Hoboken, NJ
• (wann): 2023

Weitere Informationen

• DOI: doi:10.1111/jtsa.12716
• Letzte Aktualisierung: 10.03.2025, 11:41 MEZ