AN INVARIANCE PRINCIPLE FOR SIEVE BOOTSTRAP IN TIME SERIES
Joon Park ()
Econometric Theory, 2002, vol. 18, issue 2, 469-490
This paper establishes an invariance principle applicable for the asymptotic analysis of sieve bootstrap in time series. The sieve bootstrap is based on the approximation of a linear process by a finite autoregressive process of order increasing with the sample size, and resampling from the approximated autoregression. In this context, we prove an invariance principle for the bootstrap samples obtained from the approximated autoregressive process. It is of the strong form and holds almost surely for all sample realizations. Our development relies upon the strong approximation and the Beveridgeâ€“Nelson representation of linear processes. For illustrative purposes, we apply our results and show the asymptotic validity of the sieve bootstrap for Dickeyâ€“Fuller unit root tests for the model driven by a general linear process with independent and identically distributed innovations. We thus provide a theoretical justification on the use of the bootstrap Dickeyâ€“Fuller tests for general unit root models, in place of the testing procedures by Said and Dickey and by Phillips.
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