Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-27T18:44:03.518Z Has data issue: false hasContentIssue false
  • English
  • Français

HAC ESTIMATION BY AUTOMATED REGRESSION

Published online by Cambridge University Press:  08 February 2005

Peter C.B. Phillips
Peter C.B. Phillips
Affiliation:
Cowles Foundation, Yale University University of Auckland and University of York
Get access Rights & Permissions [Opens in a new window]

Abstract

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.My thanks go to Bruce Hansen, Guido Kuersteiner, and two referees for comments on an earlier version of the paper. NSF research support under grant SES 00-92509 is acknowledged.

Type
Research Article
Information
Econometric Theory , Volume 21 , Issue 1 , February 2005 , pp. 116 - 142
Copyright
© 2005 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Andrews, D.W.K. (1991) Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica 59, 817–858.Google Scholar
Andrews, D.W.K. & J.C. Monahan (1992) An improved heteroskedasticity and autocorrelation consistent covariance matrix estimator. Econometrica 60, 953–966.Google Scholar
Den Haan, W.J. & A. Levin (1997) A practitioner's guide to robust covariance matrix estimation. In G.S. Maddala & C.R. Rao (eds.), Handbook of Statistics, vol. 15, pp. 299–342. Elsevier.
Grenander, U. & M. Rosenblatt (1957) Statistical Analysis of Stationary Time Series. Wiley.
Hannan, E.J. (1970) Multiple Time Series. Wiley.
Lee, J.S. (1996) On the power of stationary tests using optimal bandwidth estimates. Economics Letters 51, 131–137.Google Scholar
Lee, C.C. & P.C.B. Phillips (1994) An ARMA Prewhitened Long-Run Variance Estimator. Manuscript, Yale University.
Newey, W.K. & K.D. West (1987) A simple positive semi-definite heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica 55, 703–708.Google Scholar
Newey, W.K. & K.D. West (1994) Automatic lag selection in covariance matrix estimation. Review of Economic Studies 61, 631–653.Google Scholar
Phillips, P.C.B. (1996) Spurious Regression Unmasked. Cowles Foundation Discussion paper 1135, Yale University.
Phillips, P.C.B. (1998) New tools for understanding spurious regressions. Econometrica 66, 1299–1326.Google Scholar
Phillips, P.C.B. (1999) Unit Root Log Periodogram Regression. Cowles Foundation paper 1244, Yale University.
Phillips, P.C.B. (2004) Challenges of Trending Time Series Econometrics. Mimeo, Yale University.
Phillips, P.C.B. & V. Solo (1992) Asymptotics for linear processes. Annals of Statistics 20, 971–1001.Google Scholar
Phillips, P.C.B., Y. Sun, & S. Jin (2003) Consistent HAC Estimation and Robust Regression Testing Using Sharp Origin Kernels with No Truncation. Cowles Foundation Discussion paper 1407, Yale University.
Priestley, M.B. (1981) Spectral Analysis and Time Series, vol. I. Academic Press.
Sul, D., P.C.B. Phillips, & C.-Y. Choi (2003) Prewhitening Bias in HAC Estimation. Mimeo, Yale University.