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Biometrika 1983 70(2):389-399; doi:10.1093/biomet/70.2.389
© 1983 by Biometrika Trust
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Bias of some commonly-used time series estimates

DAG TJØSTHEIM and JOSTEIN PAULSEN

Department of Mathematics, University of Bergen Bergen, Norway

We study the bias of Yule-Walker and least squares estimates for univariate and multivariate autoregressive processes. We obtain explicit formulae for the large-sample bias of YuleWalker estimates in the scalar first- and second-order cases and for least squares estimates in the general case. Both simulations and theory indicate that Yule-Walker estimates are inferior to least squares estimates. For strongly autocorrelated processes, Yule-Walker estimates can be severely biased even for comparatively large-sample sizes.

Key Words: Autoregressive process • Bias • Least squares estimate • Yule—Walker estimate


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