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Spectral Analysis With Tapered Data

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  • Rainer Dahlhaus

Abstract

. A new method based on an upper bound for spectral windows is presented for investigating the cumulants of time series statistics. Using this method two classical results are proved for tapered data. In particular, the asymptotic normality for a class of spectral estimates including estimates for the spectral function and the covariance function is proved under integrability conditions on the spectra using the method of cumulants.

Suggested Citation

  • Rainer Dahlhaus, 1983. "Spectral Analysis With Tapered Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(3), pages 163-175, May.
    • Handle: RePEc:bla:jtsera:v:4:y:1983:i:3:p:163-175
    DOI: 10.1111/j.1467-9892.1983.tb00366.x
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    Cited by:

    1. Arthur P. Guillaumin & Adam M. Sykulski & Sofia C. Olhede & Frederik J. Simons, 2022. "The Debiased Spatial Whittle likelihood," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(4), pages 1526-1557, September.
    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. 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.
    4. Yoshihiro Yajima & Yasumasa Matsuda, 2023. "Gaussian semiparametric estimation Gaussian semiparametric estimation of two-dimensional intrinsically stationary random fields," DSSR Discussion Papers 136, Graduate School of Economics and Management, Tohoku University.
    5. Rainer Sachs, 1994. "Estimating non-linear functions of the spectral density, using a data-taper," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(3), pages 453-474, September.
    6. 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.
    7. Kakizawa, Yoshihide, 2007. "Moderate deviations for quadratic forms in Gaussian stationary processes," Journal of Multivariate Analysis, Elsevier, vol. 98(5), pages 992-1017, May.
    8. Fryzlewicz, Piotr & Nason, Guy P. & von Sachs, Rainer, 2008. "A wavelet-Fisz approach to spectrum estimation," LSE Research Online Documents on Economics 25186, London School of Economics and Political Science, LSE Library.
    9. Vetter, Mathias, 2014. "Inference on the Lévy measure in case of noisy observations," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 125-133.
    10. Piotr Fryzlewicz & Guy P. Nason & Rainer Von Sachs, 2008. "A wavelet‐Fisz approach to spectrum estimation," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(5), pages 868-880, September.
    11. van Delft, Anne & Eichler, Michael, 2017. "Locally Stationary Functional Time Series," LIDAM Discussion Papers ISBA 2017023, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    12. 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.
    13. 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.
    14. Evangelos E. Ioannidis, 2022. "A new non‐parametric cross‐spectrum estimator," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(5), pages 808-827, September.
    15. Jin, Lei, 2011. "A data-driven test to compare two or multiple time series," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2183-2196, June.
    16. Eichler, Michael, 2008. "Testing nonparametric and semiparametric hypotheses in vector stationary processes," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 968-1009, May.
    17. Sourav Das & Suhasini Subba Rao & Junho Yang, 2021. "Spectral methods for small sample time series: A complete periodogram approach," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(5-6), pages 597-621, September.

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