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A note on prediction and an autoregressive sequence. (English) Zbl 0787.60049

Cambanis, Stamatis (ed.) et al., Stochastic processes: a Festschrift in honour of Gopinath Kallianpur. New York: Springer-Verlag. 291-295 (1993).
The main interest of the paper is to study the behaviour of a first-order autoregressive non-Gaussian process with respect to the prediction problem. It is proved that the best one-step predictor with time reversed for a process is linear iff the corresponding distribution is Gaussian. For a non-Gaussian process an evaluation of the prediction error variance is obtained. Special cases are discussed.
For the entire collection see [Zbl 0917.00020].

MSC:

60G25 Prediction theory (aspects of stochastic processes)
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