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Prewhitening Bias in HAC Estimation

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Author Info
Peter C.B. Phillips () (Yale University, Cowles Foundation)
Chi-Young Choi () (University of New Hampshire, Department of Economics)
Donggyu Sul () (University of Auckland, Faculty of Business & Economics, Department of Economics)

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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 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).

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Paper provided by Yale School of Management in its series Yale School of Management Working Papers with number ysm426.

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Date of creation: 28 Jul 2004
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Handle: RePEc:ysm:somwrk:ysm426

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Related research
Keywords: Bias HAC estimator KPSS testing long run variance prewhitening recursive demeaning

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C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models

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  1. Nelson C. Mark & Donggyu Sul, 2004. "The Use of Predictive Regressions at Alternative Horizons in Finance and Economics," Finance 0409032, EconWPA. [Downloadable!]
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  2. Hjalmarsson, Erik, 2005. "Predictive regressions with panel data," Working Papers in Economics 160, Göteborg University, Department of Economics. [Downloadable!]
  3. Jönsson, Kristian, 2006. "Testing Stationarity in Small and Medium-Sized Samples when Disturbances are Serially Correlated," Working Papers 2006:20, Lund University, Department of Economics. [Downloadable!]
  4. Erik Hjalmarsson, 2006. "Predictive regressions with panel data," International Finance Discussion Papers 869, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
  5. Eiji Kurozumi & Kazuhiko Hayakawa, 2006. "Asymptotic Properties of the Efficient Estimators for Cointegrating Regression Models with Serially Dependent Errors," Hi-Stat Discussion Paper Series d06-197, Institute of Economic Research, Hitotsubashi University. [Downloadable!]
  6. Josep Lluís Carrion-i-Silvestre & Vicente German-Soto, 2008. "Panel Data Stochastic Convergence Analysis of the Mexican Regions," IREA Working Papers 200805, University of Barcelona, Research Institute of Applied Economics, revised Apr 2008. [Downloadable!]
  7. Donggyu Sul, 2005. "New Panel Unit Root Tests under Cross Section Dependence for Practitioners," Econometrics 0506010, EconWPA. [Downloadable!]
  8. Westerlund, Joakim, 2003. "Feasible Estimation in Cointegrated Panels," Working Papers 2003:12, Lund University, Department of Economics, revised 10 Nov 2003.
  9. Mariam Camarero & Josep Lluis Carrion Silvestre & Cecilio Tamarit, 2006. "New evidence of the real interest rate parity for OECD countries using panel unit root tests with breaks," Working Papers in Economics 159, Universitat de Barcelona. Espai de Recerca en Economia. [Downloadable!]
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  10. Jönsson , Kristian, 2006. "Finite-Sample Stability of the KPSS Test," Working Papers 2006:23, Lund University, Department of Economics. [Downloadable!]
  11. Peter C.B. Phillips & Yixiao Sun & Sainan Jin, 2005. "Improved HAR Inference," Cowles Foundation Discussion Papers 1513, Cowles Foundation, Yale University. [Downloadable!]
  12. Paulo M. M. Rodrigues, 2004. "Properties of Recursive Trend-Adjusted Unit Root Tests," Economics Working Papers ECO2004/31, European University Institute. [Downloadable!]
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  13. Peter C.B. Phillips, 2004. "HAC Estimation by Automated Regression," Cowles Foundation Discussion Papers 1470, Cowles Foundation, Yale University. [Downloadable!]
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  14. Kazuhiko Hayakawa, 2006. "A Note on Bias in First-Differenced AR(1) Models," Economics Bulletin, Economics Bulletin, vol. 3(27), pages 1-10. [Downloadable!]
  15. Peter C.B. Phillips, 2004. "Automated Discovery in Econometrics," Cowles Foundation Discussion Papers 1469, Cowles Foundation, Yale University. [Downloadable!]
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  16. Syed A. Basher & Josep Lluís Carrion-i-Silvestre, 2007. "Another Look at the Null of Stationary RealExchange Rates. Panel Data with Structural Breaks and Cross-section Dependence," IREA Working Papers 200710, University of Barcelona, Research Institute of Applied Economics, revised May 2007. [Downloadable!]
  17. Chi-Young Choi & Ling Hu & Masao Ogaki, 2005. "Structural Spurious Regressions and A Hausman-type Cointegration Test," RCER Working Papers 517, University of Rochester - Center for Economic Research (RCER). [Downloadable!]
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