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An Invariance Principle For Sieve Bootstrap In Time Series

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Author Info
Park, Joon Y.
Abstract

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 Beveridge Nelson representation of linear processes. For illustrative purposes, we apply our results and show the asymptotic validity of the sieve bootstrap for Dickey 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 Dickey Fuller tests for general unit root models, in place of the testing procedures by Said and Dickey and by Phillips.

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File URL: http://journals.cambridge.org/abstract_S0266466602182090
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Publisher Info
Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 18 (2002)
Issue (Month): 02 (May)
Pages: 469-490
Download reference. The following formats are available: HTML, plain text, BibTeX, RIS (EndNote), ReDIF
Handle: RePEc:cup:etheor:v:18:y:2002:i:02:p:469-490

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  1. Wagner, Martin & Hlouskova, Jaroslava, 2007. "The Performance of Panel Cointegration Methods. Results from a Large Scale Simulation Study," Economics Series 210, Institute for Advanced Studies. [Downloadable!]
  2. Christophe Rault & Antonio Alfonso, 2007. "What do we really know about fiscal sustainability in the EU? A panel data diagnostic," William Davidson Institute Working Papers Series wp893, William Davidson Institute at the University of Michigan Stephen M. Ross Business School. [Downloadable!]
  3. Dees, S. & Holly, S. & Pesaran, M.H. & Smith, L.V., 2007. "Long Run Macroeconomic Relations in the Global Economy," Cambridge Working Papers in Economics 0661, Faculty of Economics, University of Cambridge. [Downloadable!]
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  4. Patrick Richard, 2007. "Sieve bootstrap unit root tests," Cahiers de recherche 07-05, Departement d'Economique de la Faculte d'administration à l'Universite de Sherbrooke. [Downloadable!]
  5. António Afonso & Christophe Rault, 2008. "What do we really Know about Fiscal Sustainability in the EU? A Panel Data Diagnostic," CESifo Working Paper Series CESifo Working Paper No. , CESifo GmbH. [Downloadable!]
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  6. Imed Drine & Christophe Rault, 2008. "Purchasing Power Parity for Developing and Developed Countries. What can we Learn from Non-Stationary Panel Data Models?," CESifo Working Paper Series CESifo Working Paper No. , CESifo GmbH. [Downloadable!]
  7. Lokshin Boris, 2006. "Monte-Carlo comparison of alternative estimators for dynamic panel data models," Research Memoranda 014, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
  8. António Afonso & Christophe Rault, 2007. "What We Really Know about Fiscal Sustainability in the EU? A Panel Data Diagnostic," Working Papers 2007/20, Department of Economics at the School of Economics and Management (ISEG), Technical University of Lisbon.. [Downloadable!]
  9. Carsten Trenkler, 2006. "Bootstrapping Systems Cointegration Tests with a Prior Adjustment for Deterministic Terms," SFB 649 Discussion Papers SFB649DP2006-012, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany. [Downloadable!]
  10. Myunghwan Seo, 2005. "Unit Root Test in a Threshold Autoregression: Asymptotic Theory and Residual-based Block Bootstrap," STICERD - Econometrics Paper Series /2005/484, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
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  11. Palm Franz C. & Smeekes Stephan & Urbain Jean-Pierre, 2007. "A Sieve Bootstrap Test for Cointegration in a Conditional Error Correction Model," Research Memoranda 054, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
  12. Imed Drine & Christophe Rault, 2007. "Purchasing Power Parity for Developing and Developed Countries: What Can We Learn from Non-Stationary Panel Data Models?," IZA Discussion Papers 2887, Institute for the Study of Labor (IZA). [Downloadable!]
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