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A Practical, Accurate, Information Criterion for Nth Order Markov Processes

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  • Sylvain Barde

    (OFCE - Observatoire français des conjonctures économiques (Sciences Po) - Sciences Po - Sciences Po, Sciences Po - Sciences Po, University of Kent [Canterbury])

Abstract
There centincreasein the breath of computational methodologies has been matched with a corresponding increase in the difficulty of comparing the relative explanatory power of models from different methodological lineages.In order to help address this problem a Markovian information criterion (MIC) is developed that is analogous to the Akaike information criterion (AIC) in its theoretical derivation and yet can be applied to any model able to generate simulated or predicted data,regardless of its methodology. Both the AIC and proposed MIC rely on the Kullback–Leibler (KL) distance between model predictions and real data as a measure of prediction accuracy. Instead of using the maximum likelihood approach like the AIC, the proposed MIC relies instead on the literal interpretation of the KL distance as the inefficiency of compressing real data using modelled probabilities, and therefore uses the output of a universal compression algorithm to obtain an estimate of the KL distance. Several Monte Carlo tests are carried out in order to (a) confirm the performance of the algorithm and (b) evaluate the ability of the MIC to identify the true data-generating process from a set of alternative models.

Suggested Citation

  • Sylvain Barde, 2017. "A Practical, Accurate, Information Criterion for Nth Order Markov Processes," Post-Print hal-03471817, HAL.
    • Handle: RePEc:hal:journl:hal-03471817
    DOI: 10.1007/s10614-016-9617-9
    Note: View the original document on HAL open archive server: https://sciencespo.hal.science/hal-03471817
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    More about this item

    Keywords

    AIC; Description length; Markov process; Market selection;
    All these keywords.

    JEL classification:

    • B41 - Schools of Economic Thought and Methodology - - Economic Methodology - - - Economic Methodology
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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