The influence of the nonrecent past in prediction for stochastic processes

Harold Sackrowitz

Journal of Multivariate Analysis, 1979, vol. 9, issue 2, 222-233

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.

Keywords: Stochastic; process; prediction; martingale; Markov; process; stationary; process (search for similar items in EconPapers)
Date: 1979
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