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Relevant States and Memory in Markov Chain Bootstrapping and Simulation

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

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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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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  1. Efstathios Paparoditis & Dimitris N. Politis, 2002. "The tapered block bootstrap for general statistics from stationary sequences," Econometrics Journal, Royal Economic Society, vol. 5(1), pages 131-148, June.
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  13. M. Rajarshi, 1990. "Bootstrap in Markov-sequences based on estimates of transition density," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(2), pages 253-268, June.
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  15. Buhlmann, Peter & Kunsch, Hans R., 1999. "Block length selection in the bootstrap for time series," Computational Statistics & Data Analysis, Elsevier, vol. 31(3), pages 295-310, September.
  16. Ohno, Katsuhisa & Boh, Toshitaka & Nakade, Koichi & Tamura, Takayoshi, 2016. "New approximate dynamic programming algorithms for large-scale undiscounted Markov decision processes and their application to optimize a production and distribution system," European Journal of Operational Research, Elsevier, vol. 249(1), pages 22-31.
  17. Pandelis, Dimitrios G., 2010. "Markov decision processes with multidimensional action spaces," European Journal of Operational Research, Elsevier, vol. 200(2), pages 625-628, January.
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