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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
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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

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