Prewhitening Bias in HAC Estimation

Donggyu Sul (), Peter C. B. Phillips () and Chi-Young Choi ()

No 1436, Cowles Foundation Discussion Papers from Cowles Foundation, Yale University

Abstract: HAC estimation commonly involves the use of prewhitening filters based on simple autoregressive models. In such applications, small sample bias in the estimation of autoregressive coefficients is transmitted to the recoloring filter, leading to HAC variance estimates that can be badly biased. The present paper provides an analysis of these issues using asymptotic expansions and simulations. The approach we recommend involves the use of recursive demeaning procedures that mitigate the effects of small sample autoregressive bias. Moreover, a commonly-used restriction rule on the prewhitening estimates (that first order autoregressive coefficient estimates, or largest eigenvalues, greater than 0.97 be replaced by 0.97) adversely interfers with the power of unit root and KPSS tests. We provide a new boundary condition rule that improves the size and power properties of these tests. Some illustrations are given of the effects of these adjustments on the size and power of KPSS testing. Using prewhitened HAC estimates and the new boundary condition rule, the KPSS test is consistent, in contrast to KPSS testing that uses conventional prewhitened HAC estimates (Lee, 1996).

Keywords: Autoregression; Bias; HAC estimator; KPSS testing; Long run variance; Prewhitening; Recursive demeaning (search for similar items in EconPapers)
JEL-codes: C32 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm and nep-ets
Date: Written
Note: CFP 1161.
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Published in Oxford Bulletin of Economics and Statistics (2005), 67(4): 517-546

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Related works:
Working Paper: Prewhitening Bias in HAC Estimation (2004)
Journal Article: Prewhitening Bias in HAC Estimation (2005)
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