Minimax extrapolation and autoregressive-moving average processes. (Russian) Zbl 0704.62086

Moklyachuk, M. P.

Teor. Veroyatn. Mat. Stat., Kiev 41, 66-74 (1989).

Let \(\xi\) (j) be a stationary process. Assume that the variables \(\xi\) (j) for \(j<0\) are known and that the spectral density of the process \(\xi\) (j) belongs to a given set D. The author derives the minimax estimator of the transformation \[ A_{\xi}=\sum^{\infty}_{j=0}a(j)\xi (j). \] It is shown that under some general assumptions the least favourable spectral density corresponds to an MA process.

Reviewer: J.Anděl

MSC:

62M20	Inference from stochastic processes and prediction
60G10	Stationary stochastic processes
62M10	Time series, auto-correlation, regression, etc. in statistics (GARCH)

Keywords:

ARMA models; stationary process; minimax estimator; transformation; least favourable spectral density