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HAC Estimation by Automated Regression

A simple regression approach to HAC and LRV estimation is suggested. The method exploits the fact that the quantities of interest relate to only one point of the spectrum (the origin). The new estimator is simply the explained sum of squares in a linear regression whose regressors are a set of trend basis functions. Positive definiteness in the estimate is therefore automatically enforced and the technique can be implemented with standard regression packages. No kernel choice is needed in practical implementation but basis functions need to be chosen and a smoothing parameter corresponding to the number of basis functions needs to be selected. An automated approach to making this selection based on optimizing the asymptotic mean squared error is derived. The limit theory of the new estimator shows that its properties, including the convergence rate, are comparable to those of conventional HAC estimates constructed from quadratic kernels.

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File URL: http://cowles.econ.yale.edu/P/cd/d14b/d1470.pdf
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Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1470.

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Length: 24 pages
Date of creation: Jul 2004
Date of revision:
Publication status: Published in Econometric Theory (2005), 21(1): 116-147
Handle: RePEc:cwl:cwldpp:1470
Note: CFP 1158
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Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.econ.yale.edu/

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Order Information: Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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  1. Peter C.B. Phillips, 1996. "Spurious Regression Unmasked," Cowles Foundation Discussion Papers 1135, Cowles Foundation for Research in Economics, Yale University.
  2. Peter C.B. Phillips, 2004. "Challenges of Trending Time Series Econometrics," Cowles Foundation Discussion Papers 1472, Cowles Foundation for Research in Economics, Yale University.
  3. Newey, Whitney K & West, Kenneth D, 1987. "A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix," Econometrica, Econometric Society, vol. 55(3), pages 703-08, May.
  4. Phillips, Peter C.B., 2007. "Unit root log periodogram regression," Journal of Econometrics, Elsevier, vol. 138(1), pages 104-124, May.
  5. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-66, July.
  6. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  7. Peter C.B. Phillips & Chi-Young Choi & Donggyu Sul, 2004. "Prewhitening Bias in HAC Estimation," Yale School of Management Working Papers ysm426, Yale School of Management.
  8. Peter C. B. Phillips, 1998. "New Tools for Understanding Spurious Regressions," Econometrica, Econometric Society, vol. 66(6), pages 1299-1326, November.
  9. Newey, W.K. & West, K.D., 1992. "Automatic Lag Selection in Covariance Matrix Estimation," Working papers 9220, Wisconsin Madison - Social Systems.
  10. Wouter J. Den Haan & Andrew T. Levin, 1996. "A Practitioner's Guide to Robust Covariance Matrix Estimation," NBER Technical Working Papers 0197, National Bureau of Economic Research, Inc.
  11. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
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