IDEAS home Printed from https://ideas.repec.org/p/ehl/lserod/315.html
   My bibliography  Save this paper

Edgeworth expansions for spectral density estimates and studentized sample mean

Author

Listed:
  • Velasco, Carlos
  • Robinson, Peter M.

Abstract

We establish valid Edgeworth expansions for the distribution of smoothed nonparametric spectral estimates, and of studentized versions of linear statistics such as the sample mean, where the studentization employs such a nonparametric spectral estimate. Particular attention is paid to the spectral estimate at zero frequency and, correspondingly, the studentized sample mean, to reflect econometric interest in autocorrelation-consistent or long-run variance estimation. Our main focus is on stationary Gaussian series, though we discuss relaxation of the Gaussianity assumption. Only smoothness conditions on the spectral density that are local to the frequency of interest are imposed. We deduce empirical expansions from our Edgeworth expansions designed to improve on the normal approximation in practice and also deduce a feasible rule of bandwidth choice.

Suggested Citation

  • Velasco, Carlos & Robinson, Peter M., 2001. "Edgeworth expansions for spectral density estimates and studentized sample mean," LSE Research Online Documents on Economics 315, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:315
    as

    Download full text from publisher

    File URL: http://eprints.lse.ac.uk/315/
    File Function: Open access version.
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Taniguchi, Masanobu & Puri, Madan L., 1996. "Valid Edgeworth Expansions of M-Estimators in Regression Models with Weakly Dependent Resfduals," Econometric Theory, Cambridge University Press, vol. 12(2), pages 331-346, June.
    2. Daniel Janas, 1994. "Edgeworth expansions for spectral mean estimates with applications to Whittle estimates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(4), pages 667-682, December.
    3. Andrew Harvey (ed.), 1994. "Time Series," Books, Edward Elgar Publishing, volume 0, number 599.
    4. Robinson, P M, 1991. "Automatic Frequency Domain Inference on Semiparametric and Nonparametric Models," Econometrica, Econometric Society, vol. 59(5), pages 1329-1363, September.
    5. P. C. B. Phillips, 1980. "Finite Sample Theory and the Distributions of Alternative Estimators of the Marginal Propensity to Consume," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(1), pages 183-224.
    6. Phillips, Peter C B, 1977. "Approximations to Some Finite Sample Distributions Associated with a First-Order Stochastic Difference Equation," Econometrica, Econometric Society, vol. 45(2), pages 463-485, March.
    7. Robinson, P. M., 1995. "The approximate distribution of nonparametric regression estimates," Statistics & Probability Letters, Elsevier, vol. 23(2), pages 193-201, May.
    8. Taniguchi, Masanobu, 1987. "Validity of Edgeworth expansions of minimum contrast estimators for Gaussian ARMA processes," Journal of Multivariate Analysis, Elsevier, vol. 21(1), pages 1-28, February.
    9. Rainer Dahlhaus, 1983. "Spectral Analysis With Tapered Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(3), pages 163-175, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Peter M Robinson & Carlos Velasco, 2000. "Edgeworth Expansions for Spectral Density Estimates and Studentized Sample Mean - (Now published in Economic Theory, 17 (2001), pp.497-539," STICERD - Econometrics Paper Series 390, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    2. Sun, Yixiao X & Phillips, Peter C. B. & Jin, Sainan, 2005. "Optimal Bandwidth Selection in Heteroskedasticity-Autocorrelation Robust Testing∗," University of California at San Diego, Economics Working Paper Series qt16b3j2hd, Department of Economics, UC San Diego.
    3. Eichler, Michael, 2008. "Testing nonparametric and semiparametric hypotheses in vector stationary processes," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 968-1009, May.
    4. Phillips, Peter C.B., 2003. "Vision And Influence In Econometrics: John Denis Sargan," Econometric Theory, Cambridge University Press, vol. 19(3), pages 495-511, June.
    5. Daniel Janas & Rainer von Sachs, 1995. "Consistency For Non‐Linear Functions Of The Periodogram Of Tapered Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(6), pages 585-606, November.
    6. 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.
    7. Kourogenis, Nikolaos & Pittis, Nikitas & Samartzis, Panagiotis, 2024. "Unbounded heteroscedasticity in autoregressive models," The Journal of Economic Asymmetries, Elsevier, vol. 29(C).
    8. Arvanitis Stelios & Demos Antonis, 2018. "On the Validity of Edgeworth Expansions and Moment Approximations for Three Indirect Inference Estimators," Journal of Econometric Methods, De Gruyter, vol. 7(1), pages 1-38, January.
    9. Neil R. Ericsson, 1987. "Monte Carlo methodology and the finite sample properties of statistics for testing nested and non-nested hypotheses," International Finance Discussion Papers 317, Board of Governors of the Federal Reserve System (U.S.).
    10. Peter C. B. Phillips, 2021. "Pitfalls in Bootstrapping Spurious Regression," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 163-217, December.
    11. Hendry, David F., 1984. "Monte carlo experimentation in econometrics," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 16, pages 937-976, Elsevier.
    12. Kakizawa, Yoshihide, 2007. "Moderate deviations for quadratic forms in Gaussian stationary processes," Journal of Multivariate Analysis, Elsevier, vol. 98(5), pages 992-1017, May.
    13. Chambers, Marcus J. & Ercolani, Joanne S. & Taylor, A.M. Robert, 2014. "Testing for seasonal unit roots by frequency domain regression," Journal of Econometrics, Elsevier, vol. 178(P2), pages 243-258.
    14. Wang, Fangfang, 2014. "Optimal design of Fourier estimator in the presence of microstructure noise," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 708-722.
    15. Wouter J. Den Haan & Andrew T. Levin, 1995. "Inferences from parametric and non-parametric covariance matrix estimation procedures," International Finance Discussion Papers 504, Board of Governors of the Federal Reserve System (U.S.).
    16. Matthew Higgins & Daniel Levy & Andrew T. Young, 2003. "Growth and Convergence across the US: Evidence from County-Level Data," Working Papers 2003-03, Bar-Ilan University, Department of Economics.
    17. Müller, Ulrich K. & Wang, Yulong, 2019. "Nearly weighted risk minimal unbiased estimation," Journal of Econometrics, Elsevier, vol. 209(1), pages 18-34.
    18. Bunzel, Helle, 2006. "FIXED-b ASYMPTOTICS IN SINGLE-EQUATION COINTEGRATION MODELS WITH ENDOGENOUS REGRESSORS," Econometric Theory, Cambridge University Press, vol. 22(4), pages 743-755, August.
    19. Catherine Kyrtsou & Michel Terraza, 2003. "Is it Possible to Study Chaotic and ARCH Behaviour Jointly? Application of a Noisy Mackey–Glass Equation with Heteroskedastic Errors to the Paris Stock Exchange Returns Series," Computational Economics, Springer;Society for Computational Economics, vol. 21(3), pages 257-276, June.
    20. Javier Hidalgo, 2003. "A Bootstrap Causality Test for Covariance Stationary Processes," STICERD - Econometrics Paper Series 462, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.

    More about this item

    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics

    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:ehl:lserod:315. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: LSERO Manager (email available below). General contact details of provider: https://edirc.repec.org/data/lsepsuk.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.