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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.

Suggested Citation

  • Cerqueti, Roy & Falbo, Paolo & Pelizzari, Cristian, 2013. "Relevant States and Memory in Markov Chain Bootstrapping and Simulation," MPRA Paper 46250, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:46250
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    References listed on IDEAS

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    1. repec:eee:appene:v:195:y:2017:i:c:p:738-753 is not listed on IDEAS

    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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