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Estimation of General Stationary Processes by Variable Length Markov Chains

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  • Fiorenzo Ferrari
  • Abraham Wyner

Abstract

We develop new results about a sieve methodology for the estimation of minimal state spaces and probability laws in the class of stationary processes defined on finite categorical spaces. Using a sieve approximation with variable length Markov chains of increasing order, we show that an adapted version of the Context algorithm yields asymptotically correct estimates for the minimal state space and for the underlying probability distribution. As a side product, the method of sieves yields a nice graphical tree representation for the potentially infinite dimensional minimal state space of the data generating process, which is very useful for exploration of the memory.

Suggested Citation

  • Fiorenzo Ferrari & Abraham Wyner, 2003. "Estimation of General Stationary Processes by Variable Length Markov Chains," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(3), pages 459-480, September.
    • Handle: RePEc:bla:scjsta:v:30:y:2003:i:3:p:459-480
    DOI: 10.1111/1467-9469.00342
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    Cited by:

    1. Löcherbach, Eva & Orlandi, Enza, 2011. "Neighborhood radius estimation for variable-neighborhood random fields," Stochastic Processes and their Applications, Elsevier, vol. 121(9), pages 2151-2185, September.

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