IDEAS home Printed from https://ideas.repec.org/p/cdl/ucsdec/qt6164c110.html
   My bibliography  Save this paper

Spectral Density and Spectral Distribution Inference for Long Memory Time Series via Fixed-b Asymptotics

Author

Listed:
  • McElroy, Tucker
  • Politis, Dimitris

Abstract

Recent work in econometrics has provided large bandwidth asymptotic theory for taper-based studentized estimates of the mean, in the context of nonparametric estimation for serially correlated time series data. These taper-based statistics can be viewed as estimates of the spectral density at frequency zero, and hence it is quite natural to extend the asymptotic theory to non-zero frequencies and thereby obtain a large bandwidth theory for spectarl estimation. This approach was developed by Hashimzade and Vogelsang (2008) for the case of a single frequency. This paper extends their work in several ways: (i) we treat multiple frequencies jointly; (ii) we allow for long-range dependence at differing frequencies; (iii) we allow for piecewise smooth tapers, such as trapezoidal tapers; (iv) we develop a theory of higher order accuracy by a novel expansion of the Laplace Transform of the limit distribution. The theoretical results are complemented by simulations of the limit distributions, an application to confidence band construction, and a discussion of the issue of optimal bandwidth selection.

Suggested Citation

  • McElroy, Tucker & Politis, Dimitris, 2013. "Spectral Density and Spectral Distribution Inference for Long Memory Time Series via Fixed-b Asymptotics," University of California at San Diego, Economics Working Paper Series qt6164c110, Department of Economics, UC San Diego.
  • Handle: RePEc:cdl:ucsdec:qt6164c110
    as

    Download full text from publisher

    File URL: https://www.escholarship.org/uc/item/6164c110.pdf;origin=repeccitec
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Yixiao Sun & Peter C. B. Phillips & Sainan Jin, 2008. "Optimal Bandwidth Selection in Heteroskedasticity-Autocorrelation Robust Testing," Econometrica, Econometric Society, vol. 76(1), pages 175-194, January.
    2. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005. "A New Asymptotic Theory For Heteroskedasticity-Autocorrelation Robust Tests," Econometric Theory, Cambridge University Press, vol. 21(06), pages 1130-1164, December.
    3. Nigar Hashimzade & Timothy J. Vogelsang, 2008. "Fixed‐b asymptotic approximation of the sampling behaviour of nonparametric spectral density estimators," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(1), pages 142-162, January.
    4. Velasco, Carlos & Robinson, Peter M., 2001. "Edgeworth Expansions For Spectral Density Estimates And Studentized Sample Mean," Econometric Theory, Cambridge University Press, vol. 17(03), pages 497-539, June.
    5. Bell, William R & Hillmer, Steven C, 1984. "Issues Involved with the Seasonal Adjustment of Economic Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(4), pages 291-320, October.
    6. Findley, David F, et al, 1998. "New Capabilities and Methods of the X-12-ARIMA Seasonal-Adjustment Program," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(2), pages 127-152, April.
    7. 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.
    8. Peter C. B. Phillips & Yixiao Sun & Sainan Jin, 2006. "Spectral Density Estimation And Robust Hypothesis Testing Using Steep Origin Kernels Without Truncation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(3), pages 837-894, August.
    9. McElroy, Tucker & Politis, Dimitris N., 2012. "Fixed-B Asymptotics For The Studentized Mean From Time Series With Short, Long, Or Negative Memory," Econometric Theory, Cambridge University Press, vol. 28(02), pages 471-481, April.
    10. Peter C. B. Phillips, 1998. "New Tools for Understanding Spurious Regressions," Econometrica, Econometric Society, vol. 66(6), pages 1299-1326, November.
    11. Findley, David F, et al, 1998. "New Capabilities and Methods of the X-12-ARIMA Seasonal-Adjustment Program: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(2), pages 169-177, April.
    12. Nicholas M. Kiefer & Timothy J. Vogelsang, 2002. "Heteroskedasticity-Autocorrelation Robust Standard Errors Using The Bartlett Kernel Without Truncation," Econometrica, Econometric Society, vol. 70(5), pages 2093-2095, September.
    13. Grether, D M & Nerlove, M, 1970. "Some Properties of 'Optimal' Seasonal Adjustment," Econometrica, Econometric Society, vol. 38(5), pages 682-703, September.
    14. Mohamed Boutahar, 2008. "Identification of Persistent Cycles in Non‐Gaussian Long‐Memory Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(4), pages 653-672, July.
    15. Dahlhaus, Rainer, 1985. "Asymptotic normality of spectral estimates," Journal of Multivariate Analysis, Elsevier, vol. 16(3), pages 412-431, June.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. McElroy, Tucker S. & Holan, Scott H., 2016. "Computation of the autocovariances for time series with multiple long-range persistencies," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 44-56.

    More about this item

    Keywords

    Social and Behavioral Sciences; Cyclical Long Memory; Kernel Spectral Estimator; Long Range Dependence; Spectral Confidence Bands;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

    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:cdl:ucsdec:qt6164c110. 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: (Lisa Schiff). General contact details of provider: http://edirc.repec.org/data/deucsus.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.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with 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.