Bootstrap confidence regions computed from autoregressions of arbitrary order

Edwin Choi and Peter Hall

Journal of the Royal Statistical Society Series B, 2000, vol. 62, issue 2, 461-477

Abstract: Given a linear time series, e.g. an autoregression of infinite order, we may construct a finite order approximation and use that as the basis for confidence regions. The sieve or autoregressive bootstrap, as this method is often called, is generally seen as a competitor with the better‐understood block bootstrap approach. However, in the present paper we argue that, for linear time series, the sieve bootstrap has significantly better performance than blocking methods and offers a wider range of opportunities. In particular, since it does not corrupt second‐order properties then it may be used in a double‐bootstrap form, with the second bootstrap application being employed to calibrate a basic percentile method confidence interval. This approach confers second‐order accuracy without the need to estimate variance. That offers substantial benefits, since variances of statistics based on time series can be difficult to estimate reliably, and—partly because of the relatively small amount of information contained in a dependent process—are notorious for causing problems when used to Studentize. Other advantages of the sieve bootstrap include considerably greater robustness against variations in the choice of the tuning parameter, here equal to the autoregressive order, and the fact that, in contradistinction to the case of the block bootstrap, the percentile t version of the sieve bootstrap may be based on the ‘raw'’ estimator of standard error. In the process of establishing these properties we show that the sieve bootstrap is second order correct.

Date: 2000
References: Add references at CitEc
Citations: View citations in EconPapers (21)

Downloads: (external link)
https://doi.org/10.1111/1467-9868.00244

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:jorssb:v:62:y:2000:i:2:p:461-477

Ordering information: This journal article can be ordered from
http://ordering.onli ... 1111/(ISSN)1467-9868

Access Statistics for this article

Journal of the Royal Statistical Society Series B is currently edited by P. Fryzlewicz and I. Van Keilegom

More articles in Journal of the Royal Statistical Society Series B from Royal Statistical Society Contact information at EDIRC.
Bibliographic data for series maintained by Wiley Content Delivery ().