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