Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/290181 
Year of Publication: 
2023
Citation: 
[Journal:] Journal of Time Series Analysis [ISSN:] 1467-9892 [Volume:] 45 [Issue:] 3 [Publisher:] Wiley [Place:] Hoboken, NJ [Year:] 2023 [Pages:] 361-375
Publisher: 
Wiley, Hoboken,NJ
Abstract: 
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.
Subjects: 
Autocovariance
time series
Wasserstein distance
Stein's method
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by-nc Logo
Document Type: 
Article
Document Version: 
Published Version
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