Block Bootstrap Theory for Multivariate Integrated and Cointegrated Processes

26 Pages Posted: 24 Apr 2015

See all articles by Carsten Jentsch

Carsten Jentsch

University of Mannheim

Dimitris N. Politis

University of California, San Diego (UCSD) - Department of Mathematics

Efstathios Paparoditis

University of Cyprus - Department of Mathematics and Statistics

Date Written: May 2015

Abstract

We develop some asymptotic theory for applications of block bootstrap resampling schemes to multivariate integrated and cointegrated time series. It is proved that a multivariate, continuous‐path block bootstrap scheme applied to a full rank integrated process succeeds in estimating consistently the distribution of the least squares estimators in both the regression and the spurious regression case. Furthermore, it is shown that the same block resampling scheme does not succeed in estimating the distribution of the parameter estimators in the case of cointegrated time series. For this situation, a modified block resampling scheme, the so‐called residual‐based block bootstrap, is investigated, and its validity for approximating the distribution of the regression parameters is established. The performance of the proposed block bootstrap procedures is illustrated in a short simulation study.

Keywords: Block bootstrap, bootstrap consistency, spurious regression, functional limit theorem, continuous‐path block bootstrap, model‐based block bootstrap subclass

Suggested Citation

Jentsch, Carsten and Politis, Dimitris and Paparoditis, Efstathios, Block Bootstrap Theory for Multivariate Integrated and Cointegrated Processes (May 2015). Recent developments in bootstrap methods for dependent data, Vol. 36, Issue 3, pp. 416-441, 2015, Available at SSRN: https://ssrn.com/abstract=2598287 or http://dx.doi.org/10.1111/jtsa.12088

Carsten Jentsch (Contact Author)

University of Mannheim

Dimitris Politis

University of California, San Diego (UCSD) - Department of Mathematics ( email )

9500 Gilman Drive
La Jolla, CA 92093-0112
United States
858-534-5861 (Phone)
858-534-5273 (Fax)

Efstathios Paparoditis

University of Cyprus - Department of Mathematics and Statistics ( email )

P.O. Box 20537
1678 Nicosia
Cyprus
00357-2-338701 (Phone)
00357-2-339061 (Fax)

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