IDEAS home Printed from https://ideas.repec.org/p/cwl/cwldpp/1407.html
   My bibliography  Save this paper

Consistent HAC Estimation and Robust Regression Testing Using Sharp Origin Kernels with No Truncation

Author

Listed:

Abstract

A new family of kernels is suggested for use in heteroskedasticity and autocorrelation consistent (HAC) and long run variance (LRV) estimation and robust regression testing. The kernels are constructed by taking powers of the Bartlett kernel and are intended to be used with no truncation (or bandwidth) parameter. As the power parameter (rho) increases, the kernels become very sharp at the origin and increasingly downweight values away fro the origin, thereby achieving effects similar to a bandwidth parameter. Sharp origin kernels can be used in regression testing in much the same way as conventional kernels with no truncation, as suggested in the work of Kiefer and Vogelsang (2002a, 2002b). A unified representation of HAC limit theory for untruncated kernels is provided using a new proof based on Mercer's theorem that allows for kernels which may or may not be differentiable at the origin. This new representation helps to explain earlier findings like the dominance of the Bartlett kernel over quadratic kernels in test power and yields new findings about the asymptotic properties of tests with sharp origin kernels. Analysis and simulations indicate that sharp origin kernels lead to tests with improved size properties relative to conventional tests and better power properties than other tests using Bartlett and other conventional kernels without truncation. If rho is passed to infinity with the sample size (T), the new kernels provide consistent HAC and LRV estimates as well as continued robust regression testing. Optimal choice of rho based on minimizing the asymptotic mean squared error of estimation is considered, leading to a rate of convergence of the kernel estimate of T^{1/3}, analogous to that of a conventional truncated Bartlett kernel estimate with an optimal choice of bandwidth. A data-based version of the consistent sharp origin kernel is obtained which is easily implementable in practical work. Within this new framework, untruncated kernel estimation can be regarded as a form of conventional kernel estimation in which the usual bandwidth parameter is replaced by a power parameter that serves to control the degree of downweighting. Simulations show that in regression testing with the sharp origin kernel, the power properties are better than those with simple untruncated kernels (where rho = 1) and at least as good as those with truncated kernels. Size is generally more accurate with sharp origin kernels than truncated kernels. In practice a simple fixed choice of the exponent parameter around rho = 16 for the sharp origin kernel produces favorable results for both size and power in regression testing with sample sizes that are typical in econometric applications.

Suggested Citation

  • 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.
  • Handle: RePEc:cwl:cwldpp:1407
    as

    Download full text from publisher

    File URL: http://cowles.yale.edu/sites/default/files/files/pub/d14/d1407.pdf
    Download Restriction: no

    Other versions of this item:

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Surajit Ray & N. E. Savin, 2008. "The performance of heteroskedasticity and autocorrelation robust tests: a Monte Carlo study with an application to the three-factor Fama-French asset-pricing model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(1), pages 91-109.
    3. Thieu, Le Quyen, 2016. "Variance targeting estimation of the BEKK-X model," MPRA Paper 75572, University Library of Munich, Germany.
    4. Harding, Don & Pagan, Adrian, 2006. "Synchronization of cycles," Journal of Econometrics, Elsevier, vol. 132(1), pages 59-79, May.
    5. Bernard Fingleton & Michelle Catherine Baddeley, 2011. "Globalisation And Wage Differentials: A Spatial Analysis," Manchester School, University of Manchester, vol. 79(5), pages 1018-1034, September.
    6. João Valle e Azevedo, 2011. "Rational vs. professional forecasts," Economic Bulletin and Financial Stability Report Articles and Banco de Portugal Economic Studies, Banco de Portugal, Economics and Research Department.
    7. Peter C.B. Phillips & Yixiao Sun & Sainan Jin, 2005. "Improved HAR Inference," Cowles Foundation Discussion Papers 1513, Cowles Foundation for Research in Economics, Yale University.
    8. Hansen, Christian B., 2007. "Asymptotic properties of a robust variance matrix estimator for panel data when T is large," Journal of Econometrics, Elsevier, vol. 141(2), pages 597-620, December.
    9. Thieu, Le Quyen, 2016. "Equation by equation estimation of the semi-diagonal BEKK model with covariates," MPRA Paper 75582, University Library of Munich, Germany.
    10. Jen-Je Su, 2005. "On the size and power of testing for no autocorrelation under weak assumptions," Applied Financial Economics, Taylor & Francis Journals, vol. 15(4), pages 247-257.

    More about this item

    Keywords

    Consistent HAC estimation; Data determined kernel estimation; Long run variance; Mercer?s theorem; Power parameter; Sharp origin kernel;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cwl:cwldpp:1407. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Matthew Regan). General contact details of provider: http://edirc.repec.org/data/cowleus.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.