Simultaneous inference for autocovariances based on autoregressive sieve bootstrap

Artikel

In this article, maximum deviations of sample autocovariances and autocorrelations from their theoretical counterparts over an increasing set of lags are considered. The asymptotic distribution of such statistics for physically dependent stationary time series, which is of Gumbel type, only depends on second‐order properties of the underlying time series. Since the autoregressive sieve bootstrap is able to mimic the second‐order structure asymptotically correctly it is an obvious problem whether the autoregressive (AR) sieve bootstrap, which has been shown to work for a number of relevant statistics in time series analysis, asymptotically works for maximum deviations of autocovariances and autocorrelations as well. This article shows that the question can be answered positively. Moreover, potential applications including spectral density estimation and an investigation of finite sample properties of the AR‐sieve bootstrap proposal by simulation are given.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Journal: Journal of Time Series Analysis ; ISSN: 1467-9892 ; Volume: 42 ; Year: 2021 ; Issue: 5-6 ; Pages: 534-553 ; Oxford, UK: John Wiley & Sons, Ltd

Classification and Topics

• Subject: Autocovariance ; autoregressive sieve bootstrap ; stationary process ; spectral density ; simultaneous confidence bands

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Braumann, Alexander ; Kreiss, Jens‐Peter ; Meyer, Marco
• Event: Veröffentlichung
• (who): John Wiley & Sons, Ltd
• (where): Oxford, UK
• (when): 2021

Further information

• DOI: doi:10.1111/jtsa.12604
• Handle: http://hdl.handle.net/10419/284790
• Last update: 10.03.2025, 11:42 AM CET