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Higher-order accurate, positive semi-definite estimation of large-sample covariance and spectral density matrices

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Author Info
Dimitris Politis (University of California, San Diego)
Abstract

A new class of HAC covariance matrix estimators is proposed based on the notion of a flat-top kernel as in Politis and Romano (1995)and Politis (2001). The new estimators are shown to be higher-order accurate when higher-order accuracy is possible, and a discussion on kernel choice is given. The higher-order accuracy of flat-top kernel estimators typically comes at the sacrifice of the positive semi-definite property. Nevertheless, we show how a modified flat-top estimator is positive semi-definite while maintaining its higher-order accuracy. In addition, an automatic and consistent procedure for optimal bandwidth choice for flat-top kernel HAC estimators is given. The general problem of spectral matrix estimation is also treated.

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Paper provided by Department of Economics, UC San Diego in its series University of California at San Diego, Economics Working Paper Series with number 2005-03.

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Date of creation: 01 Mar 2005
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Handle: RePEc:cdl:ucsdec:2005-03

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Keywords: HAC estimations; spectral estimation;

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  1. 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. [Downloadable!] (restricted)
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  2. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May. [Downloadable!] (restricted)
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  3. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July. [Downloadable!] (restricted)
  4. Robinson, P M, 1991. "Automatic Frequency Domain Inference on Semiparametric and Nonparametric Models," Econometrica, Econometric Society, vol. 59(5), pages 1329-63, September. [Downloadable!] (restricted)
  5. Newey, Whitney K & West, Kenneth D, 1994. "Automatic Lag Selection in Covariance Matrix Estimation," Review of Economic Studies, Blackwell Publishing, vol. 61(4), pages 631-53, October. [Downloadable!] (restricted)
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  6. 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. [Downloadable!] (restricted)
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  7. Hansen, Bruce E, 1992. "Consistent Covariance Matrix Estimation for Dependent Heterogeneous Processes," Econometrica, Econometric Society, vol. 60(4), pages 967-72, July. [Downloadable!] (restricted)
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