COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1436

"Prewhitening Bias in HAC Estimation"

Donggyu Sul
Department of Economics, University of Auckland
Peter C.B. Phillips
Cowles Foundation, Yale University, University of Auckland and University of York
Chi-Young Choi
Department of Economics, University of New Hampshire

September 2003

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 interferes 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

JEL Classification Numbers: C32 Time Series Models