Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-05T13:26:52.955Z Has data issue: false hasContentIssue false
  • English
  • Français

AUTOMATIC POSITIVE SEMIDEFINITE HAC COVARIANCE MATRIX AND GMM ESTIMATION

Published online by Cambridge University Press:  08 February 2005

Richard J. Smith
Richard J. Smith
Affiliation:
cemmap, U.C.L. and I.F.S. and University of Warwick
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper proposes a new class of heteroskedastic and autocorrelation consistent (HAC) covariance matrix estimators. The standard HAC estimation method reweights estimators of the autocovariances. Here we initially smooth the data observations themselves using kernel function–based weights. The resultant HAC covariance matrix estimator is the normalized outer product of the smoothed random vectors and is therefore automatically positive semidefinite. A corresponding efficient GMM criterion may also be defined as a quadratic form in the smoothed moment indicators whose normalized minimand provides a test statistic for the overidentifying moment conditions.

Type
Research Article
Information
Econometric Theory , Volume 21 , Issue 1 , February 2005 , pp. 158 - 170
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
Bierens, H.J. (1997) Nonparametric cointegration analysis. Journal of Econometrics 77, 379–404.Google Scholar
Brillinger, D.R. (1981) Time Series: Data Analysis and Theory. Holden-Day.
Grenander, U. & M. Rosenblatt (1984) Statistical Analysis of Stationary Time Series. Chelsea.
Hansen, L.P. (1982) Large sample properties of generalized method of moments estimators. Econometrica 50, 1029–1054.Google Scholar
Hansen, L.P., J. Heaton, & A. Yaron (1996) Finite-sample properties of some alternative GMM estimators. Journal of Business & Economic Statistics 14, 262–280.Google Scholar
Jansson, M. (2002) Consistent covariance matrix estimation for linear processes. Econometric Theory 18, 1449–1459.Google Scholar
Kiefer, N.M., T.J. Vogelsang, & H. Bunzel (2000) Simple robust testing of regression hypotheses. Econometrica 68, 695–714.Google Scholar
Kitamura, Y. & M. Stutzer (1997) An information-theoretic alternative to generalized method of moments estimation. Econometrica 65, 861–874.Google Scholar
Newey, W.K. (1985) Generalized method of moments specification testing. Journal of Econometrics 29, 229–256.Google Scholar
Newey, W.K. & D. McFadden (1994) Large sample estimation and hypothesis testing. In R.F. Engle and D. McFadden (eds.), Handbook of Econometrics, vol. 4, 2111–2245. North-Holland.
Newey, W.K. & K.D. West (1987a) A simple, positive semi-definite heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica 55, 703–708.Google Scholar
Newey, W.K. & K.D. West (1987b) Hypothesis testing with efficient method of moments estimation. International Economic Review 28, 777–787.Google Scholar
Parzen, E. (1957) On consistent estimates of the spectrum of a stationary time series. Annals of Mathematical Statistics 28, 329–348.Google Scholar
Phillips, P.C.B. (2005) HAC estimation by automated regression. Econometric Theory (this issue).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. (1962) Basic considerations in the estimation of spectra. Technometrics 4, 551–564.Google Scholar
Smith, R.J. (1997) Alternative semi-parametric likelihood approaches to generalized method of moments estimation. Economic Journal 107, 503–519.Google Scholar
Smith, R.J. (2001) GEL Criteria for Moment Condition Models. Working paper, University of Bristol.
Thomson, D.J. (1982) Spectrum estimation and harmonic analysis. Proceedings of the IEEE 70, 1055–1096.Google Scholar
Walden, A.T. (2000) A unified view of multitaper multivariate spectral estimation. Biometrika 87, 767–788.Google Scholar
White, H. (1984) Asymptotic Theory for Econometricians. Academic Press.