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Prewhitening Bias in HAC Estimation

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Author Info
Donggyu Sul
Peter C. B. Phillips
Chi-Young Choi

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Abstract

Heteroskedasticity and autocorrelation consistent (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 recolouring 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, >0.97 be replaced by 0.97) adversely interferes with the power of unit-root and [Kwiatkowski, Phillips, Schmidt and Shin (1992) "Journal of Econometrics", Vol. 54, pp. 159-178] (KPSS) tests. We provide a new boundary condition rule that improves the size and power properties of these tests. Some illustrations of the effects of these adjustments on the size and power of KPSS testing are given. 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, J. S. (1996) "Economics Letters", Vol. 51, pp. 131-137]. Copyright 2005 Blackwell Publishing Ltd.

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Article provided by Department of Economics, University of Oxford in its journal Oxford Bulletin of Economics & Statistics.

Volume (Year): 67 (2005)
Issue (Month): 4 (08)
Pages: 517-546
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Handle: RePEc:bla:obuest:v:67:y:2005:i:4:p:517-546

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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. Peter C.B. Phillips & Yixiao Sun & Sainan Jin, 2005. "Improved HAR Inference," Cowles Foundation Discussion Papers 1513, Cowles Foundation, Yale University. [Downloadable!]
  3. Hjalmarsson, Erik, 2005. "Predictive regressions with panel data," Working Papers in Economics 160, Göteborg University, Department of Economics. [Downloadable!]
  4. 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!]
  5. Mark J. Holmes & Theodore Panagiotidis & Jesus Otero, 2008. "Are EU budgets stationary?," Discussion Paper Series 2008_07, Department of Economics, University of Macedonia, revised Sep 2008. [Downloadable!]
  6. 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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  7. Erik Hjalmarsson, 2006. "Predictive regressions with panel data," International Finance Discussion Papers 869, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
  8. Syed A. Basher & Josep Lluis Carrión-i-Silvestre, 2008. "Price level convergence, purchasing power parity and multiple structural breaks: An application to US cities," Working Papers XREAP2008-8, Xarxa de Referència en Economia Aplicada (XREAP), revised Jul 2008. [Downloadable!]
  9. 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!]
  10. 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!]
  11. Peter C.B. Phillips, 2004. "HAC Estimation by Automated Regression," Cowles Foundation Discussion Papers 1470, Cowles Foundation, Yale University. [Downloadable!]
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  12. Donggyu Sul, 2005. "New Panel Unit Root Tests under Cross Section Dependence for Practitioners," Econometrics 0506010, EconWPA. [Downloadable!]
  13. Kazuhiko Hayakawa, 2006. "A Note on Bias in First-Differenced AR(1) Models," Economics Bulletin, Economics Bulletin, vol. 3(27), pages 1-10. [Downloadable!]
  14. Westerlund, Joakim, 2003. "Feasible Estimation in Cointegrated Panels," Working Papers 2003:12, Lund University, Department of Economics, revised 10 Nov 2003.
  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. 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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  18. Jönsson , Kristian, 2006. "Finite-Sample Stability of the KPSS Test," Working Papers 2006:23, Lund University, Department of Economics. [Downloadable!]
  19. 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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