IDEAS home Printed from https://ideas.repec.org/p/ysm/somwrk/ysm427.html
   My bibliography  Save this paper

Long Run Variance Estimation Using Steep Origin Kernels Without Truncation

Author

Listed:
  • Peter C.B. Phillips

    () (Yale University, Cowles Foundation)

  • Sainan Jin

    () (Yale University, Faculty of Arts & Sciences, Department of Economics (Box 8268))

  • Yixiao Sun

    () (University of California, San Diego, Division of Social Sciences, Department of Economics)

Abstract

A new class of kernel estimates is proposed for long run variance (LRV) and heteroskedastic autocorrelation consistent (HAC) estimation. The kernels are called steep origin kernels and are related to a class of sharp origin kernels explored by the authors (2003) in other work. They are constructed by exponentiating a mother kernel (a conventional lag kernel that is smooth at the origin) and they can be used without truncation or bandwidth parameters. When the exponent is passed to infinity with the sample size, these kernels produce consistent LRV/HAC estimates. The new estimates are shown to have limit normal distributions, and formulae for the asymptotic bias and variance are derived. With steep origin kernel estimation, bandwidth selection is replaced by exponent selection and data-based selection is possible. Rules for exponent selection based on minimum mean squared error (MSE)\ criteria are developed. Optimal rates for steep origin kernels that are based on exponentiating quadratic kernels are shown to be faster than those based on exponentiating the Bartlett kernel, which produces the sharp origin kernel. It is further shown that, unlike conventional kernel estimation where an optimal choice of kernel is possible in terms of MSE\ criteria (Priestley, 1962; Andrews, 1991), steep origin kernels are asymptotically MSE equivalent, so that choice of mother kernel does not matter asymptotically. The approach is extended to spectral estimation at frequencies \omega \neq 0. Some simulation evidence is reported detailing the finite sample performance of steep kernel methods in LRV/HAC estimation and robust regression testing in comparison with sharp kernel and conventional (truncated) kernel methods.

Suggested Citation

  • Peter C.B. Phillips & Sainan Jin & Yixiao Sun, 2004. "Long Run Variance Estimation Using Steep Origin Kernels Without Truncation," Yale School of Management Working Papers ysm427, Yale School of Management.
  • Handle: RePEc:ysm:somwrk:ysm427
    as

    Download full text from publisher

    File URL: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=446684
    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. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Designing Realized Kernels to Measure the ex post Variation of Equity Prices in the Presence of Noise," Econometrica, Econometric Society, vol. 76(6), pages 1481-1536, November.
    2. 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.

    More about this item

    Keywords

    Exponentiated kernel; lag kernel; long run variance; optimal exponent; spectral window; spectrum;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    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:ysm:somwrk:ysm427. 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: (). General contact details of provider: http://edirc.repec.org/data/smyalus.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.