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.

Object Details

• Language: Englisch

References and Relationships

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

Classification and Topics

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

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Anastasiou, Andreas ; Kley, Tobias
• Event: Veröffentlichung
• (who): Wiley
• (where): Hoboken, NJ
• (when): 2023

Further information

• DOI: doi:10.1111/jtsa.12716
• Last update: 10.03.2025, 11:41 AM CET