Adaptive Estimation of Autoregressive Models with Time-Varying Variances

Ke-Li Xu () and Peter C. B. Phillips ()

No 1585R, Cowles Foundation Discussion Papers from Cowles Foundation, Yale University

Abstract: Stable autoregressive models of known finite order are considered with martingale differences errors scaled by an unknown nonparametric time-varying function generating heterogeneity. An important special case involves structural change in the error variance, but in most practical cases the pattern of variance change over time is unknown and may involve shifts at unknown discrete points in time, continuous evolution or combinations of the two. This paper develops kernel-based estimators of the residual variances and associated adaptive least squares (ALS) estimators of the autoregressive coefficients. These are shown to be asymptotically efficient, having the same limit distribution as the infeasible generalized least squares (GLS). Comparisons of the efficient procedure and ordinary least squares (OLS) reveal that least squares can be extremely inefficient in some cases while nearly optimal in others. Simulations show that, when least squares work well, the adaptive estimators perform comparably well, whereas when least squares work poorly, major efficiency gains are achieved by the new estimators.

Keywords: Adaptive estimation; Autoregression; Heterogeneity; Weighted regression (search for similar items in EconPapers)
JEL-codes: C14 C22 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ict
Date: 2006-10, Revised 2006-11
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Published in Journal of Econometrics (2008), 142: 265-280

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Related works:
Working Paper: Adaptive Estimation of Autoregressive Models with Time-Varying Variances (2006)
Journal Article: Adaptive estimation of autoregressive models with time-varying variances (2008)
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