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. Velasco, Carlos & Robinson, Peter M., 2001. "Edgeworth Expansions For Spectral Density Estimates And Studentized Sample Mean," Econometric Theory, Cambridge University Press, vol. 17(3), pages 497-539, June.
    3. 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.
    4. 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.
    5. 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(2), pages 471-481, April.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Grether, D M & Nerlove, M, 1970. "Some Properties of 'Optimal' Seasonal Adjustment," Econometrica, Econometric Society, vol. 38(5), pages 682-703, September.
    11. Bell, William R & Hillmer, Steven C, 1984. "Issues Involved with the Seasonal Adjustment of Time Series: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(4), pages 343-349, October.
    12. 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.
    13. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005. "A New Asymptotic Theory For Heteroskedasticity-Autocorrelation Robust Tests," Econometric Theory, Cambridge University Press, vol. 21(6), pages 1130-1164, December.
    14. McElroy, Tucker & Politis, Dimitris N., 2013. "Distribution theory for the studentized mean for long, short, and negative memory time series," Journal of Econometrics, Elsevier, vol. 177(1), pages 60-74.
    15. 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.
    16. Henry L. Gray & Nien‐Fan Zhang & Wayne A. Woodward, 1989. "On Generalized Fractional Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 10(3), pages 233-257, May.
    17. Peter C. B. Phillips, 1998. "New Tools for Understanding Spurious Regressions," Econometrica, Econometric Society, vol. 66(6), pages 1299-1326, November.
    18. Dahlhaus, Rainer, 1985. "Asymptotic normality of spectral estimates," Journal of Multivariate Analysis, Elsevier, vol. 16(3), pages 412-431, June.
    19. 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)

    Citations

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


    Cited by:

    1. McElroy, Tucker S. & Jach, Agnieszka, 2023. "Identification of the differencing operator of a non-stationary time series via testing for zeroes in the spectral density," Computational Statistics & Data Analysis, Elsevier, vol. 177(C).
    2. Tucker S. McElroy & Anindya Roy, 2022. "Model identification via total Frobenius norm of multivariate spectra," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(2), pages 473-495, April.
    3. Tucker McElroy & Anindya Roy, 2022. "A Review of Seasonal Adjustment Diagnostics," International Statistical Review, International Statistical Institute, vol. 90(2), pages 259-284, August.
    4. 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.
    5. van Delft, Anne & Eichler, Michael, 2020. "A note on Herglotz’s theorem for time series on function spaces," Stochastic Processes and their Applications, Elsevier, vol. 130(6), pages 3687-3710.
    6. Tucker S McElroy & Agnieszka Jach, 2019. "Testing collinearity of vector time series," The Econometrics Journal, Royal Economic Society, vol. 22(2), pages 97-116.

    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. McElroy, Tucker & Politis, Dimitris N., 2013. "Distribution theory for the studentized mean for long, short, and negative memory time series," Journal of Econometrics, Elsevier, vol. 177(1), pages 60-74.
    2. Xiaofeng Shao, 2010. "A self‐normalized approach to confidence interval construction in time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 343-366, June.
    3. Politis, D N, 2009. "Higher-Order Accurate, Positive Semi-definite Estimation of Large-Sample Covariance and Spectral Density Matrices," University of California at San Diego, Economics Working Paper Series qt66w826hz, Department of Economics, UC San Diego.
    4. Sun, Yixiao & Phillips, Peter C.B. & Jin, Sainan, 2011. "Power Maximization And Size Control In Heteroskedasticity And Autocorrelation Robust Tests With Exponentiated Kernels," Econometric Theory, Cambridge University Press, vol. 27(6), pages 1320-1368, December.
    5. Preinerstorfer, David & Pötscher, Benedikt M., 2016. "On Size And Power Of Heteroskedasticity And Autocorrelation Robust Tests," Econometric Theory, Cambridge University Press, vol. 32(2), pages 261-358, April.
    6. Hirukawa, Masayuki, 2023. "Robust Covariance Matrix Estimation in Time Series: A Review," Econometrics and Statistics, Elsevier, vol. 27(C), pages 36-61.
    7. Pötscher, Benedikt M. & Preinerstorfer, David, 2018. "Controlling the size of autocorrelation robust tests," Journal of Econometrics, Elsevier, vol. 207(2), pages 406-431.
    8. Sun, Yixiao, 2011. "Robust trend inference with series variance estimator and testing-optimal smoothing parameter," Journal of Econometrics, Elsevier, vol. 164(2), pages 345-366, October.
    9. Muller, Ulrich K., 2007. "A theory of robust long-run variance estimation," Journal of Econometrics, Elsevier, vol. 141(2), pages 1331-1352, December.
    10. Ray, Surajit & Savin, N.E. & Tiwari, Ashish, 2009. "Testing the CAPM revisited," Journal of Empirical Finance, Elsevier, vol. 16(5), pages 721-733, December.
    11. Kolokotrones, Thomas & Stock, James H. & Walker, Christopher D., 2024. "Is Newey–West optimal among first-order kernels?," Journal of Econometrics, Elsevier, vol. 240(2).
    12. Casini, Alessandro, 2024. "The fixed-b limiting distribution and the ERP of HAR tests under nonstationarity," Journal of Econometrics, Elsevier, vol. 238(2).
    13. Xu, Ke-Li, 2012. "Robustifying multivariate trend tests to nonstationary volatility," Journal of Econometrics, Elsevier, vol. 169(2), pages 147-154.
    14. Kai Wenger & Christian Leschinski & Philipp Sibbertsen, 2019. "Change-in-mean tests in long-memory time series: a review of recent developments," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(2), pages 237-256, June.
    15. Federico Belotti & Alessandro Casini & Leopoldo Catania & Stefano Grassi & Pierre Perron, 2023. "Simultaneous bandwidths determination for DK-HAC estimators and long-run variance estimation in nonparametric settings," Econometric Reviews, Taylor & Francis Journals, vol. 42(3), pages 281-306, February.
    16. M. Angeles Carnero & Siem Jan Koopman & Marius Ooms, 2003. "Periodic Heteroskedastic RegARFIMA Models for Daily Electricity Spot Prices," Tinbergen Institute Discussion Papers 03-071/4, Tinbergen Institute.
    17. Han, Heejoon & Linton, Oliver & Oka, Tatsushi & Whang, Yoon-Jae, 2016. "The cross-quantilogram: Measuring quantile dependence and testing directional predictability between time series," Journal of Econometrics, Elsevier, vol. 193(1), pages 251-270.
    18. Kim, Min Seong & Sun, Yixiao & Yang, Jingjing, 2017. "A fixed-bandwidth view of the pre-asymptotic inference for kernel smoothing with time series data," Journal of Econometrics, Elsevier, vol. 197(2), pages 298-322.
    19. Matei Demetrescu & Christoph Hanck & Robinson Kruse, 2016. "Fixed-b Inference in the Presence of Time-Varying Volatility," CREATES Research Papers 2016-01, Department of Economics and Business Economics, Aarhus University.
    20. Sun, Yixiao, 2014. "Let’s fix it: Fixed-b asymptotics versus small-b asymptotics in heteroskedasticity and autocorrelation robust inference," Journal of Econometrics, Elsevier, vol. 178(P3), pages 659-677.

    More about this item

    Keywords

    Social and Behavioral Sciences; Cyclical Long Memory; Kernel Spectral Estimator; Long Range Dependence; Spectral Confidence Bands;
    All these keywords.

    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.

    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: Lisa Schiff (email available below). General contact details of provider: https://edirc.repec.org/data/deucsus.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.