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).
Sul, Donggyu; Phillips, Peter C.B.; and Choi, Chi-Young, "Prewhitening Bias in HAC Estimation" (2003). Cowles Foundation Discussion Papers. 1711.