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Relevant States and Memory in Markov Chain Bootstrapping and Simulation

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  • Cerqueti, Roy
  • Falbo, Paolo
  • Pelizzari, Cristian

Abstract

Markov chain theory is proving to be a powerful approach to bootstrap highly nonlinear time series. In this work we provide a method to estimate the memory of a Markov chain (i.e. its order) and to identify its relevant states. In particular the choice of memory lags and the aggregation of irrelevant states are obtained by looking for regularities in the transition probabilities. Our approach is based on an optimization model. More specifically we consider two competing objectives that a researcher will in general pursue when dealing with bootstrapping: preserving the “structural” similarity between the original and the simulated series and assuring a controlled diversification of the latter. A discussion based on information theory is developed to define the desirable properties for such optimal criteria. Two numerical tests are developed to verify the effectiveness of the method proposed here.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 46250.

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Date of creation: 2013
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Handle: RePEc:pra:mprapa:46250

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Keywords: Bootstrapping; Information Theory; Markov chains; Optimization; Simulation.;

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  1. Buhlmann, Peter & Kunsch, Hans R., 1999. "Block length selection in the bootstrap for time series," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 31(3), pages 295-310, September.
  2. Stanislav Anatolyev & Andrey Vasnev, 2002. "Markov chain approximation in bootstrapping autoregressions," Economics Bulletin, AccessEcon, vol. 3(19), pages 1-8.
  3. Brock, William & Lakonishok, Josef & LeBaron, Blake, 1992. " Simple Technical Trading Rules and the Stochastic Properties of Stock Returns," Journal of Finance, American Finance Association, American Finance Association, vol. 47(5), pages 1731-64, December.
  4. Joel L. Horowitz, 2003. "Bootstrap Methods for Markov Processes," Econometrica, Econometric Society, Econometric Society, vol. 71(4), pages 1049-1082, 07.
  5. Ryan Sullivan & Allan Timmermann & Halbert White, 1999. "Data-Snooping, Technical Trading Rule Performance, and the Bootstrap," Journal of Finance, American Finance Association, American Finance Association, vol. 54(5), pages 1647-1691, October.
  6. Patrice Bertail & Stéphan Clémençon, 2007. "Second-order properties of regeneration-based bootstrap for atomic Markov chains," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, Springer, vol. 16(1), pages 109-122, May.
  7. M. Rajarshi, 1990. "Bootstrap in Markov-sequences based on estimates of transition density," Annals of the Institute of Statistical Mathematics, Springer, Springer, vol. 42(2), pages 253-268, June.
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