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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 and simulate 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 and simulation: preserving the “structural” similarity between the original and the resampled 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 proposed method.

Suggested Citation

  • Cerqueti, Roy & Falbo, Paolo & Pelizzari, Cristian, 2017. "Relevant states and memory in Markov chain bootstrapping and simulation," European Journal of Operational Research, Elsevier, vol. 256(1), pages 163-177.
  • Handle: RePEc:eee:ejores:v:256:y:2017:i:1:p:163-177
    DOI: 10.1016/j.ejor.2016.06.006
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    1. Stanislav Anatolyev & Andrey Vasnev, 2002. "Markov chain approximation in bootstrapping autoregressions," Economics Bulletin, AccessEcon, vol. 3(19), pages 1-8.
    2. 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.
    3. Chao, Gary H., 2013. "Production and availability policies through the Markov Decision Process and myopic methods for contractual and selective orders," European Journal of Operational Research, Elsevier, vol. 225(3), pages 383-392.
    4. Ryan Sullivan & Allan Timmermann & Halbert White, 1999. "Data-Snooping, Technical Trading Rule Performance, and the Bootstrap," Journal of Finance, American Finance Association, vol. 54(5), pages 1647-1691, October.
    5. 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.
    6. White, D. J., 1987. "Infinite horizon Markov decision processes with unknown or variable discount factors," European Journal of Operational Research, Elsevier, vol. 28(1), pages 96-100, January.
    7. Paparoditis, Efstathios & Politis, Dimitris N., 2001. "A Markovian Local Resampling Scheme For Nonparametric Estimators In Time Series Analysis," Econometric Theory, Cambridge University Press, vol. 17(03), pages 540-566, June.
    8. 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.
    9. repec:ebl:ecbull:v:3:y:2002:i:19:p:1-8 is not listed on IDEAS
    10. José M. Bernardo & Raúl Rueda, 2002. "Bayesian Hypothesis Testing: a Reference Approach," International Statistical Review, International Statistical Institute, vol. 70(3), pages 351-372, December.
    11. Brock, William & Lakonishok, Josef & LeBaron, Blake, 1992. " Simple Technical Trading Rules and the Stochastic Properties of Stock Returns," Journal of Finance, American Finance Association, vol. 47(5), pages 1731-1764, December.
    12. Hall, Peter, 1985. "Resampling a coverage pattern," Stochastic Processes and their Applications, Elsevier, vol. 20(2), pages 231-246, September.
    13. 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;Sociedad de Estadística e Investigación Operativa, vol. 16(1), pages 109-122, May.
    14. White, Chelsea C. & White, Douglas J., 1989. "Markov decision processes," European Journal of Operational Research, Elsevier, vol. 39(1), pages 1-16, March.
    15. 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.
    16. Dimitris Politis & Halbert White, 2004. "Automatic Block-Length Selection for the Dependent Bootstrap," Econometric Reviews, Taylor & Francis Journals, vol. 23(1), pages 53-70.
    17. Joel L. Horowitz, 2003. "Bootstrap Methods for Markov Processes," Econometrica, Econometric Society, vol. 71(4), pages 1049-1082, July.
    18. 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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    More about this item

    Keywords

    Bootstrapping; Information theory; Markov chains; Optimization; Simulation;

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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