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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 heteroskedastic and autocorrelation consistent (HAC) covariance matrix estimators. The standard HAC estimation method reweights 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 normalized outer product of the smoothed random vectors and is therefore automatically positive semidefinite. A corresponding efficient GMM criterion may also be defined as a quadratic form in the smoothed moment indicators whose normalized minimand provides a test statistic for the overidentifying moment conditions.

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 21 (2005)
Issue (Month): 01 (February)
Pages: 158-170

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Handle: RePEc:cup:etheor:v:21:y:2005:i:01:p:158-170_05

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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.
  2. 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 262-80, July.
  3. Jansson, Michael, 2002. "Consistent Covariance Matrix Estimation For Linear Processes," Econometric Theory, Cambridge University Press, vol. 18(06), pages 1449-1459, December.
  4. 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.
  5. Sainan Jin & Peter Phillips & Yixiao Sun, 2004. "Consistent HAC Estimation and Robust Regression Testing Using Sharp Origin Kernels with No Truncation," Econometric Society 2004 North American Winter Meetings 299, Econometric Society.
  6. 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.
  7. Bierens, Herman J., 1997. "Nonparametric cointegration analysis," Journal of Econometrics, Elsevier, vol. 77(2), pages 379-404, April.
  8. 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.
  9. Peter C.B. Phillips, 2004. "HAC Estimation by Automated Regression," Cowles Foundation Discussion Papers 1470, Cowles Foundation for Research in Economics, Yale University.
  10. K. Newey, Whitney, 1985. "Generalized method of moments specification testing," Journal of Econometrics, Elsevier, vol. 29(3), pages 229-256, September.
  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. 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 777-87, October.
  13. Smith, Richard J., 2011. "Gel Criteria For Moment Condition Models," Econometric Theory, Cambridge University Press, vol. 27(06), pages 1192-1235, December.
  14. 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.
  15. Smith, Richard J, 1997. "Alternative Semi-parametric Likelihood Approaches to Generalised Method of Moments Estimation," Economic Journal, Royal Economic Society, vol. 107(441), pages 503-19, March.
  16. 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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Cited by:
  1. 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.
  2. 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.
  3. Stanislav Anatolyev, 2005. "Optimal Instruments in Time Series: A Survey," Working Papers w0069, Center for Economic and Financial Research (CEFIR).
  4. Smith, Richard J., 2011. "Gel Criteria For Moment Condition Models," Econometric Theory, Cambridge University Press, vol. 27(06), pages 1192-1235, December.
  5. Travaglini, Guido, 2010. "Dynamic Econometric Testing of Climate Change and of its Causes," MPRA Paper 23600, University Library of Munich, Germany.
  6. 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.

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