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Wavelet-based Estimation for Heteroskedasticity and Autocorrelation Consistent Variance-Covariance Matrices

  • Yongmiao Hong

    (Cornell University)

  • Jin Lee

    (Cornell University)

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    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.

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    Paper provided by Econometric Society in its series Econometric Society World Congress 2000 Contributed Papers with number 1211.

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    Date of creation: 01 Aug 2000
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    Handle: RePEc:ecm:wc2000:1211
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    1. 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.
    2. 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.
    3. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
    4. 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.
    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. 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.
    7. David K. Levine, 1983. "A Remark on Serial Correlation in Maximum Likelihood," Levine's Working Paper Archive 176, David K. Levine.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. Hansen, Bruce E, 1992. "Consistent Covariance Matrix Estimation for Dependent Heterogeneous Processes," Econometrica, Econometric Society, vol. 60(4), pages 967-72, July.
    14. White, Halbert & Domowitz, Ian, 1984. "Nonlinear Regression with Dependent Observations," Econometrica, Econometric Society, vol. 52(1), pages 143-61, January.
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