On the statistical inference of a machine-generated autoregressive AR(1) model

Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1998 · Volume 60 · Issue 4

Abstract

We have obtained the asymptotic bias and the limiting distribution for the Yule–Walker estimator of the autoregressive parameter under a considerably weaker assumption than that of independence in the noise sequence. Among other things, these suggest robustness of the classical results and throw some light on the use of simulations based on pseudorandom numbers in verifying these results.

Keywords

Absolute regularity, Autoregressive models, Bernoulli shift, Central limit theorem, Chaotic maps, Mixing, Pseudorandom numbers, U-statistics, Yule–Walker estimators

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