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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 S.
  • Politis, Dimitris N.

Abstract

This paper studies taper-based estimates of the spectral density utilizing a fixed bandwidth ratio asymptotic framework, and makes several theoretical contributions: (i) we treat multiple frequencies jointly, (ii) we allow for long-range dependence or anti-persistence at differing frequencies, (iii) we allow for tapers that are only piecewise smooth or discontinuous, including flat-top and truncation tapers, (iv) we study higher-order accuracy through the limit distribution’s Laplace Transform, (v) we develop a taper-based estimation theory for the spectral distribution, and show how confidence bands can be constructed. Simulation results produce quantiles and document the finite-sample size properties of the estimators, and a few empirical applications demonstrate the utility of the new methods.

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  • McElroy, Tucker S. & Politis, Dimitris N., 2014. "Spectral density and spectral distribution inference for long memory time series via fixed-b asymptotics," Journal of Econometrics, Elsevier, vol. 182(1), pages 211-225.
    • Handle: RePEc:eee:econom:v:182:y:2014:i:1:p:211-225
    DOI: 10.1016/j.jeconom.2014.04.019
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    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.
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    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.
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    Cited by:

    1. Tucker McElroy & Anindya Roy, 2022. "A Review of Seasonal Adjustment Diagnostics," International Statistical Review, International Statistical Institute, vol. 90(2), pages 259-284, August.
    2. Tucker S McElroy & Agnieszka Jach, 2019. "Testing collinearity of vector time series," The Econometrics Journal, Royal Economic Society, vol. 22(2), pages 97-116.
    3. 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).
    4. 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.
    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

    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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