The influence of the nonrecent past in prediction for stochastic processes

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Consider the stochastic processes X1, X2,... and Λ1, Λ2,... where the X process can be thought of as observations on the Λ process. We investigate the asymptotic behavior of the conditional distributions of Xt+v given X1,..., Xt and Λt+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.

Original languageEnglish (US)
Pages (from-to)222-233
Number of pages12
JournalJournal of Multivariate Analysis
Issue number2
StatePublished - Jun 1979

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Markov process
  • Stochastic process
  • martingale
  • prediction
  • stationary process


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