Yule-Walker estimates and asymptotic I-divergence rate. (English) Zbl 0744.62126

Michálek, J.

Probl. Control Inf. Theory 19, No. 5-6, 387-398 (1990).

Summary: The goal of the paper is to show a close connection between the Yule- Walker estimates and the so-called \(\alpha\)-estimates, which were introduced and investigated by I. Vajda [Theory of statistical inference and information (1989; Zbl 0711.62002)]. It is proved that the Yule-Walker estimates can be obtained by minimization of the asymptotic \(I\)-divergence rate between a probability measure corresponding to an autoregressive stationary random sequence and a suitable probability measure derived from observations.

MSC:

62M10	Time series, auto-correlation, regression, etc. in statistics (GARCH)
62B10	Statistical aspects of information-theoretic topics
62M15	Inference from stochastic processes and spectral analysis
62M99	Inference from stochastic processes

Keywords:

alpha estimates; spectral density; Toeplitz matrices; strong consistency; Rényi distance; Yule-Walker estimates; minimization of asymptotic \(I\)- divergence rate; autoregressive stationary random sequence