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The influence of the nonrecent past in prediction for stochastic processes

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  • Sackrowitz, Harold

Abstract

Consider the stochastic processes X1, X2,... and [Lambda]1, [Lambda]2,... where the X process can be thought of as observations on the [Lambda] process. We investigate the asymptotic behavior of the conditional distributions of Xt+v given X1,..., Xt and [Lambda]t+v given X1,..., Xt with regard to their dependency on the "early" part of the X process. These distributions arise in various time series and sequential decision theory problems. The results support the intuitively reasonable and often used (as a basic tenet of model building) assumption that only the more recent past is needed for near optimal prediction.

Suggested Citation

  • Sackrowitz, Harold, 1979. "The influence of the nonrecent past in prediction for stochastic processes," Journal of Multivariate Analysis, Elsevier, vol. 9(2), pages 222-233, June.
    • Handle: RePEc:eee:jmvana:v:9:y:1979:i:2:p:222-233
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