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Automatic Positive Semidefinite Hac Covariance Matrix And Gmm Estimation

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  • Smith, Richard J.

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.
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  • Smith, Richard J., 2005. "Automatic Positive Semidefinite Hac Covariance Matrix And Gmm Estimation," Econometric Theory, Cambridge University Press, vol. 21(01), pages 158-170, February.
  • Handle: RePEc:cup:etheor:v:21:y:2005:i:01:p:158-170_05
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    References listed on IDEAS

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    1. Phillips, Peter C.B., 2005. "Hac Estimation By Automated Regression," Econometric Theory, Cambridge University Press, vol. 21(01), pages 116-142, February.
    2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    3. Peter C.B. Phillips & Yixiao Sun & Sainan Jin, 2003. "Consistent HAC Estimation and Robust Regression Testing Using Sharp Origin Kernels with No Truncation," Cowles Foundation Discussion Papers 1407, Cowles Foundation for Research in Economics, Yale University.
    4. Smith, Richard J, 1997. "Alternative Semi-parametric Likelihood Approaches to Generalised Method of Moments Estimation," Economic Journal, Royal Economic Society, vol. 107(441), pages 503-519, March.
    5. Newey, Whitney K & West, Kenneth D, 1987. "Hypothesis Testing with Efficient Method of Moments Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(3), pages 777-787, October.
    6. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    7. Newey, Whitney K. & McFadden, Daniel, 1986. "Large sample estimation and hypothesis testing," Handbook of Econometrics,in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 36, pages 2111-2245 Elsevier.
    8. Yuichi Kitamura & Michael Stutzer, 1997. "An Information-Theoretic Alternative to Generalized Method of Moments Estimation," Econometrica, Econometric Society, vol. 65(4), pages 861-874, July.
    9. K. Newey, Whitney, 1985. "Generalized method of moments specification testing," Journal of Econometrics, Elsevier, vol. 29(3), pages 229-256, September.
    10. Nicholas M. Kiefer & Timothy J. Vogelsang & Helle Bunzel, 2000. "Simple Robust Testing of Regression Hypotheses," Econometrica, Econometric Society, vol. 68(3), pages 695-714, May.
    11. Smith, Richard J., 2011. "Gel Criteria For Moment Condition Models," Econometric Theory, Cambridge University Press, vol. 27(06), pages 1192-1235, December.
    12. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-966, July.
    13. 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.
    14. 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.
    15. Bierens, Herman J., 1997. "Nonparametric cointegration analysis," Journal of Econometrics, Elsevier, vol. 77(2), pages 379-404, April.
    16. Jansson, Michael, 2002. "Consistent Covariance Matrix Estimation For Linear Processes," Econometric Theory, Cambridge University Press, vol. 18(06), pages 1449-1459, December.
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    Citations

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    Cited by:

    1. Guggenberger, Patrik & Smith, Richard J., 2008. "Generalized empirical likelihood tests in time series models with potential identification failure," Journal of Econometrics, Elsevier, vol. 142(1), pages 134-161, January.
    2. Chu, Ba & Jacho-Chávez, David T., 2012. "k-NEAREST NEIGHBOR ESTIMATION OF INVERSE-DENSITY-WEIGHTED EXPECTATIONS WITH DEPENDENT DATA," Econometric Theory, Cambridge University Press, vol. 28(04), pages 769-803, August.
    3. repec:taf:gnstxx:v:29:y:2017:i:1:p:108-136 is not listed on IDEAS
    4. Stanislav Anatolyev, 2007. "Optimal Instruments In Time Series: A Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 21(1), pages 143-173, February.
    5. Francesco Bravo & Ba M. Chu & David T. Jacho-Chávez, 2017. "Semiparametric estimation of moment condition models with weakly dependent data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(1), pages 108-136, January.
    6. Travaglini, Guido, 2010. "Dynamic Econometric Testing of Climate Change and of its Causes," MPRA Paper 23600, University Library of Munich, Germany.
    7. Smith, Richard J., 2011. "Gel Criteria For Moment Condition Models," Econometric Theory, Cambridge University Press, vol. 27(06), pages 1192-1235, December.
    8. Guggenberger, Patrik & Ramalho, Joaquim J.S. & Smith, Richard J., 2012. "GEL statistics under weak identification," Journal of Econometrics, Elsevier, vol. 170(2), pages 331-349.
    9. Jochen Heberle & Cristina Sattarhoff, 2017. "A Fast Algorithm for the Computation of HAC Covariance Matrix Estimators," Econometrics, MDPI, Open Access Journal, vol. 5(1), pages 1-16, January.

    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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