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Automatic positive semi-definite HAC covariance matrix and GMM estimation

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  • Richard Smith

Abstract

This paper proposes a new class of HAC covariance matrix estimators. The standard HAC estimation method re-weights 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 normalised outer product of the smoothed random vectors and is therefore automatically positive semi-definite. A corresponding efficient GMM criterion may also be defined as a quadratic form in the smoothed moment indicators whose normalised minimand provides a test statistic for the over-identifying moment conditions.

Suggested Citation

  • Richard Smith, 2004. "Automatic positive semi-definite HAC covariance matrix and GMM estimation," CeMMAP working papers 17/04, Institute for Fiscal Studies.
    • Handle: RePEc:azt:cemmap:17/04
    DOI: 10.1920/wp.cem.2004.1704
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    References listed on IDEAS

    as
    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
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    9. Hansen, Lars Peter & Heaton, John & Yaron, Amir, 1996. "Finite-Sample Properties of Some Alternative GMM Estimators," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 262-280, July.
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