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Prewhitening Bias in HAC Estimation

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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).

Suggested Citation

  • Donggyu Sul & Peter C.B. Phillips & Choi, Chi-Young, 2003. "Prewhitening Bias in HAC Estimation," Cowles Foundation Discussion Papers 1436, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1436
    Note: CFP 1161.
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    File URL: http://cowles.yale.edu/sites/default/files/files/pub/d14/d1436.pdf
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    Keywords

    Autoregression; Bias; HAC estimator; KPSS testing; Long run variance; Prewhitening; Recursive demeaning;

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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