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

Rosenblatt, Murray

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].

Reviewer: I.Valuşescu (Bucureşti)

MSC:

60G25

Prediction theory (aspects of stochastic processes)

Keywords:

autoregressive sequence; non-Gaussian process; prediction error variance