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Asymptotics Of Spectral Density Estimates

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  • Liu, Weidong
  • Wu, Wei Biao

Abstract

We consider nonparametric estimation of spectral densities of stationary processes, a fundamental problem in spectral analysis of time series. Under natural and easily verifiable conditions, we obtain consistency and asymptotic normality of spectral density estimates. Asymptotic distribution of maximum deviations of the spectral density estimates is also derived. The latter result sheds new light on the classical problem of tests of white noises.

Suggested Citation

  • Liu, Weidong & Wu, Wei Biao, 2010. "Asymptotics Of Spectral Density Estimates," Econometric Theory, Cambridge University Press, vol. 26(04), pages 1218-1245, August.
  • Handle: RePEc:cup:etheor:v:26:y:2010:i:04:p:1218-1245_99
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    Cited by:

    1. Politis, Dimitris, 2012. "On The Behavior Of Nonparametric Density And Spectral Density Estimators At Zero Points Of Their Support," University of California at San Diego, Economics Working Paper Series qt40g0z0tz, Department of Economics, UC San Diego.
    2. Stefan Birr & Stanislav Volgushev & Tobias Kley & Holger Dette & Marc Hallin, 2017. "Quantile spectral analysis for locally stationary time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1619-1643, November.
    3. Forni, Mario & Hallin, Marc & Lippi, Marco & Zaffaroni, Paolo, 2017. "Dynamic factor models with infinite-dimensional factor space: Asymptotic analysis," Journal of Econometrics, Elsevier, vol. 199(1), pages 74-92.
    4. Horváth, Lajos & Rice, Gregory & Whipple, Stephen, 2016. "Adaptive bandwidth selection in the long run covariance estimator of functional time series," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 676-693.
    5. Seok Young Hong & Oliver Linton & Hui Jun Zhang, 2014. "Multivariate Variance Ratio Statistics," Cambridge Working Papers in Economics 1459, Faculty of Economics, University of Cambridge.
    6. Berkes, István & Horváth, Lajos & Rice, Gregory, 2016. "On the asymptotic normality of kernel estimators of the long run covariance of functional time series," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 150-175.
    7. Seok Young Hong & Oliver Linton & Hui Jun Zhang, 2015. "An investigation into Multivariate Variance Ratio Statistics and their application to Stock Market Predictability," Cambridge Working Papers in Economics 1552, Faculty of Economics, University of Cambridge.
    8. Horváth, Lajos & Reeder, Ron, 2012. "Detecting changes in functional linear models," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 310-334.
    9. repec:bla:scjsta:v:44:y:2017:i:4:p:866-898 is not listed on IDEAS
    10. Efstathios Paparoditis & Dimitris N. Politis, 2016. "A Note on the Behaviour of Nonparametric Density and Spectral Density Estimators at Zero Points of their Support," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(2), pages 182-194, March.

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