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Bootstrap Methods for Markov Processes

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Author Info
Joel L. Horowitz
Abstract

The block bootstrap is the best known bootstrap method for time-series data when the analyst does not have a parametric model that reduces the data generation process to simple random sampling. However, the errors made by the block bootstrap converge to zero only slightly faster than those made by first-order asymptotic approximations. This paper describes a bootstrap procedure for data that are generated by a Markov process or a process that can be approximated by a Markov process with sufficient accuracy. The procedure is based on estimating the Markov transition density nonparametrically. Bootstrap samples are obtained by sampling the process implied by the estimated transition density. Conditions are given under which the errors made by the Markov bootstrap converge to zero more rapidly than those made by the block bootstrap. Copyright The Econometric Society 2003.

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Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 71 (2003)
Issue (Month): 4 (07)
Pages: 1049-1082
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Handle: RePEc:ecm:emetrp:v:71:y:2003:i:4:p:1049-1082

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  2. Manzan, S. & Zerom, D., 2005. "A Multi-Step Forecast Density," CeNDEF Working Papers 05-05, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance. [Downloadable!]
  3. Yongmiao Hong & Yoon-Jin Lee, 2007. "Detecting Misspecifications in Autoregressive Conditional Duration Models," Caepr Working Papers 2007-019, Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington. [Downloadable!]
  4. D. S. Poskitt, 2006. "Properties of the Sieve Bootstrap for Fractionally Integrated and Non-Invertible Processes," Monash Econometrics and Business Statistics Working Papers 12/06, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
  5. Matos, Joao Amaro de & Fernandes, Marcelo, 2004. "Testing the Markov property with ultra-high frequency financial data," FEUNL Working Paper Series wp462, Universidade Nova de Lisboa, Faculdade de Economia. [Downloadable!]
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  7. Sancetta, A., 2007. "Nearest Neighbor Conditional Estimation for Harris Recurrent Markov Chains," Cambridge Working Papers in Economics 0735, Faculty of Economics, University of Cambridge. [Downloadable!]
  8. Gao, Jiti & Gijbels, Irene, 2005. "Bandwidth selection for nonparametric kernel testing," MPRA Paper 11982, University Library of Munich, Germany, revised Jun 2007. [Downloadable!]
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