Wavelet-based Estimation for Heteroskedasticity and Autocorrelation Consistent Variance-Covariance Matrices
As is well-known, a heteroskedasticity and autocorrelation consistent covariance matrix is proportional to a spectral density matrix at frequency zero and can be consistently estimated by such popular kernel methods as those of Andrews-Newey-West. In practice, it is difficult to estimate the spectral density matrix if it has a peak at frequency zero, which can arise when there is strong autocorrelation, as often encountered in economic and financial time series. Kernels, as a local averaging method, tend to underestimate the peak, thus leading to strong overrejection in testing and overly narrow confidence intervals in estimation. As a new mathematical tool generalizing Fourier transform, wavelet transform is a powerful tool to investigate such local properties as peaks and spikes, and thus is suitable for estimating covariance matrices. In this paper, we propose a class of wavelet estimators for the covariance matrices of econometric parameter estimators. We show the consistency of the wavelet-based covariance estimators and derive their asymptotic mean squared errors, which provide insight into the smoothing nature of wavelet estimation. We propose a data-driven method to select the finest scale---the smoothing parameter in wavelet estimation, making the wavelet estimators operational in practice. A simulation study compares the finite sample performances of the wavelet estimators and the kernel counterparts. As expected, the wavelet method outperforms the kernel method when there exists relatively strong autocorrelation in the data.
|Date of creation:||01 Aug 2000|
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- Hansen, Bruce E, 1992. "Consistent Covariance Matrix Estimation for Dependent Heterogeneous Processes," Econometrica, Econometric Society, vol. 60(4), pages 967-72, July.
- David K. Levine, 1983.
"A Remark on Serial Correlation in Maximum Likelihood,"
Levine's Working Paper Archive
176, David K. Levine.
- Levine, David, 1983. "A remark on serial correlation in maximum likelihood," Journal of Econometrics, Elsevier, vol. 23(3), pages 337-342, December.
- David Levine, 1981. "A Remark on Serial Correlation in Maximum Likelihood," UCLA Economics Working Papers 215, UCLA Department of Economics.
- Donald W.K. Andrews & Christopher J. Monahan, 1990.
"An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator,"
Cowles Foundation Discussion Papers
942, Cowles Foundation for Research in Economics, Yale University.
- 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.
- White, Halbert & Domowitz, Ian, 1984. "Nonlinear Regression with Dependent Observations," Econometrica, Econometric Society, vol. 52(1), pages 143-61, January.
- repec:att:wimass:9220 is not listed on IDEAS
- Lawrence J. Christiano & Wouter den Haan, 1995.
"Small sample properties of GMM for business cycle analysis,"
Working Paper Series, Macroeconomic Issues
95-3, Federal Reserve Bank of Chicago.
- Chistiano, Lawrence J & den Haan, Wouter J, 1996. "Small-Sample Properties of GMM for Business-Cycle Analysis," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 309-27, July.
- Lawrence J. Christiano & Wouter Den Haan, 1995. "Small sample properties of GMM for business cycle analysis," Staff Report 199, Federal Reserve Bank of Minneapolis.
- Lawrence J. Christiano & Wouter J. Den Haan, 1995. "Small Sample Properties of GMM for Business Cycle Analysis," NBER Technical Working Papers 0177, National Bureau of Economic Research, Inc.
- Keener, Robert W. & Kmenta, Jan & Weber, Neville C., 1991.
"Estimation of the Covariance Matrix of the Least-Squares Regression Coefficients When the Disturbance Covariance Matrix Is of Unknown Form,"
Cambridge University Press, vol. 7(01), pages 22-45, March.
- Keener, R.W. & Kmenta, J. & Weber, N.C., 1990. "Estimation of the Covariance Matrix of the Least Squares regression Coefficients when the Disturbance Covariance Matrix is of Unknown Form," Papers 90-19, Michigan - Center for Research on Economic & Social Theory.
- Kool, J.T.C., 1988. "A note on consistent estimation of heteroskedastic and autocorrelated covariance matrices," Serie Research Memoranda 0021, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
- Donald W.K. Andrews, 1988.
"Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation,"
Cowles Foundation Discussion Papers
877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
- Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
- Whitney K. Newey & Kenneth D. West, 1986.
"A Simple, Positive Semi-Definite, Heteroskedasticity and AutocorrelationConsistent Covariance Matrix,"
NBER Technical Working Papers
0055, National Bureau of Economic Research, Inc.
- 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.
- Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 33(1), pages 125-132.
- Kiefer, Nicholas M. & Bunzel, Helle & Vogelsang, Timothy & Vogelsang, Timothy & Bunzel, Helle, 2000.
"Simple Robust Testing of Regression Hypotheses,"
Staff General Research Papers
1832, Iowa State University, Department of Economics.
- Newey, Whitney K & West, Kenneth D, 1994.
"Automatic Lag Selection in Covariance Matrix Estimation,"
Review of Economic Studies,
Wiley Blackwell, vol. 61(4), pages 631-53, October.
- Kenneth D. West & Whitney K. Newey, 1995. "Automatic Lag Selection in Covariance Matrix Estimation," NBER Technical Working Papers 0144, National Bureau of Economic Research, Inc.
- Phillips, P. C. B. & Ouliaris, S., 1988. "Testing for cointegration using principal components methods," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 205-230.
- Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-38, July.
- Cochrane, John H, 1988. "How Big Is the Random Walk in GNP?," Journal of Political Economy, University of Chicago Press, vol. 96(5), pages 893-920, October.
- Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
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