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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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Find related papers by 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

References

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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.
   
   • Peter C.B. Phillips, 2004. "HAC Estimation by Automated Regression," Cowles Foundation Discussion Papers 1470, Cowles Foundation for Research in Economics, Yale University.
2. 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.
   
   • Whitney K. Newey & Kenneth D. West, 1986. "A Simple, Positive Semi-Definite, Heteroskedasticity and AutocorrelationConsistent Covariance Matrix," NBER Technical Working Papers 0055, National Bureau of Economic Research, Inc.
3. 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.
4. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
5. K. Newey, Whitney, 1985. "Generalized method of moments specification testing," Journal of Econometrics, Elsevier, vol. 29(3), pages 229-256, September.
6. 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.
   
   • 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.
7. Phillips, Peter C.B. & Sun, Yixiao & Jin, Sainan, 2004. "Consistent HAC Estimation and Robust Regression Testing Using Sharp Origin Kernels with No Truncation," University of California at San Diego, Economics Working Paper Series qt6d36x00z, Department of Economics, UC San Diego.
   
   • 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.
   • 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.
   • Peter C.B. Phillips & Sainan Jin & Yixiao Sun, 2004. "Consistent HAC Estimation and Robust Regression Testing Using Sharp Origin Kernels with No Truncation," Yale School of Management Working Papers ysm347, Yale School of Management.
8. Smith, Richard J., 2011. "Gel Criteria For Moment Condition Models," Econometric Theory, Cambridge University Press, vol. 27(06), pages 1192-1235, December.
   
   • Richard Smith, 2004. "GEL Criteria for Moment Condition Models," CeMMAP working papers CWP19/04, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
9. Bierens, Herman J., 1997. "Nonparametric cointegration analysis," Journal of Econometrics, Elsevier, vol. 77(2), pages 379-404, April.
   
   • Bierens, H.J., 1995. "Nonparametric cointegration analysis," Discussion Paper 1995-123, Tilburg University, Center for Economic Research.
10. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
    
    • 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.
11. 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.
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 953-66, July.
    
    • Donald W.K. Andrews & Christopher J. Monahan, 1990. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Cowles Foundation Discussion Papers 942, Cowles Foundation for Research in Economics, Yale University.
13. Jansson, Michael, 2002. "Consistent Covariance Matrix Estimation For Linear Processes," Econometric Theory, Cambridge University Press, vol. 18(06), pages 1449-1459, December.
14. 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.
15. 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.
16. 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.

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Citations

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Cited by:

1. Stanislav Anatolyev, 2005. "Optimal Instruments in Time Series: A Survey," Working Papers w0069, Center for Economic and Financial Research (CEFIR).
   
   • Stanislav Anatolyev, 2007. "Optimal Instruments In Time Series: A Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 21(1), pages 143-173, 02.
2. Smith, Richard J., 2011. "Gel Criteria For Moment Condition Models," Econometric Theory, Cambridge University Press, vol. 27(06), pages 1192-1235, December.
   
   • Richard Smith, 2004. "GEL Criteria for Moment Condition Models," CeMMAP working papers CWP19/04, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
3. 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.
   
   • Patrik Guggenberger & Richard Smith, 2005. "Generalized empirical likelihood tests in time series models with potential identification failure," CeMMAP working papers CWP01/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
4. Alastair R. Hall & Yuyi Li & Chris D. Orme, 2012. "Testing for Structural Instability in Moment Restriction Models: an Info?metric Approach," The School of Economics Discussion Paper Series 1205, Economics, The University of Manchester.
5. Travaglini, Guido, 2010. "Dynamic Econometric Testing of Climate Change and of its Causes," MPRA Paper 23600, University Library of Munich, Germany.

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