Relevant States and Memory in Markov Chain Bootstrapping and Simulation
AbstractMarkov 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 InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 46250.
Date of creation: 2013
Date of revision:
Bootstrapping; Information Theory; Markov chains; Optimization; Simulation.;
Find related papers by 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-04-20 (All new papers)
- NEP-ECM-2013-04-20 (Econometrics)
- NEP-ETS-2013-04-20 (Econometric Time Series)
- NEP-ORE-2013-04-20 (Operations Research)
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