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Correcting Predictive ModelCorrecting Models of Chaotic Reality

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Abstract

We will assume a chaotic (mixing) reality, can observe a substantially aggregated state vector only and want to predict one or more of its elements using a stochastic model. However, chaotic dynamics can be predicted in a short term only, while in the long term an ergodic distribution is the best predictor. Our stochastic model will thus be considered a local approximation with no predictive ability for the far future. Using an estimate of an ergodic distribution of the predicted scalar (or eventually vector), we get, under additional reasonable assumptions, the uniquely specified resulting model, containing information from both the local model and the ergodic distribution. For a small prediction horizon, if the local model converges in probability to a constant and additional technical assumption is fulfilled, the resulting model converges in L1 norm to the local model. In long term, the resulting model converges in L1 to the ergodic distribution. We propose also a formula for computing the resulting model from the nonparametric specification of the ergodic distribution (using past observations directly). Two examples follow.

Suggested Citation

  • Petr Kadeřábek, 2006. "Correcting Predictive ModelCorrecting Models of Chaotic Reality," Working Papers IES 2006/31, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, revised Dec 2006.
  • Handle: RePEc:fau:wpaper:wp2006_31
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    File URL: http://ies.fsv.cuni.cz/default/file/download/id/4955
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    1. Tomáš Cahlík, 2002. "Central and east european countries after entering the european union," Prague Economic Papers, University of Economics, Prague.
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    Keywords

    Chaotic system; Prediction; Bayesian Analysis; Local Approximation; Ergodic Distribution;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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