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

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  • 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
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    References listed on IDEAS

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    1. 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.
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    14. 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.
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    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 S McElroy & Agnieszka Jach, 2019. "Testing collinearity of vector time series," The Econometrics Journal, Royal Economic Society, vol. 22(2), pages 97-116.
    4. Tucker McElroy & Anindya Roy, 2022. "A Review of Seasonal Adjustment Diagnostics," International Statistical Review, International Statistical Institute, vol. 90(2), pages 259-284, August.
    5. 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.
    6. 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.

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    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

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