IDEAS home Printed from https://ideas.repec.org/a/bla/jtsera/v16y1995i6p585-606.html

Consistency For Non‐Linear Functions Of The Periodogram Of Tapered Data

Author

Listed:
  • Daniel Janas
  • Rainer von Sachs

Abstract

. In this paper we investigate the merits of using a data taper in non‐linear functional of the periodogram of a stationary time series. To this end, we show consistency for a general class of statistics of the form , where A(ω) is a function of bounded variation and where φ is allowed to be a non‐linear function of the periodogram IT(ω) of the tapered data. The key step in deriving our asymptotic results is an Edgeworth expansion for the finite Fourier transform of the tapered data, which do not have to follow a particular distribution (i.e. we allow for non‐Gaussianity). Important applications are the estimation of , choosing φ to be a suitable transform of a given function g (see Taniguchi, On estimation of the integrals of certain functions of spectral density. J. Appl. Prob. 17 (1980). 73–83), the peak‐insensitive spectrum estimator of von Sachs (Peak‐insensitive nonparametric spectrum estimation. J. Time Ser. Anal. 15 (1994), 429–52), where φ is chosen to be a bounded (robustifying) σ function, and the parametric approach of Chiu (Peak‐insensitive parametric spectrum estimation. Stoch. Proc. Appl. 35 (1990). 121–40) on robust estimation of the parameters of the continuous spectrum of the time series.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jtsera:v:16:y:1995:i:6:p:585-606
    DOI: 10.1111/j.1467-9892.1995.tb00257.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9892.1995.tb00257.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-9892.1995.tb00257.x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Daniel Janas, 1994. "Edgeworth expansions for spectral mean estimates with applications to Whittle estimates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(4), pages 667-682, December.
    2. Chen Zhao‐Guo & E. J. Hannan, 1980. "The Distribution Of Periodogram Ordinates," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(1), pages 73-82, January.
    3. Dahlhaus, Rainer, 1985. "Asymptotic normality of spectral estimates," Journal of Multivariate Analysis, Elsevier, vol. 16(3), pages 412-431, June.
    4. 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)

    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. 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.
    2. 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.
    3. Kakizawa, Yoshihide, 2007. "Moderate deviations for quadratic forms in Gaussian stationary processes," Journal of Multivariate Analysis, Elsevier, vol. 98(5), pages 992-1017, May.
    4. 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.
    5. 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.
    6. Mahmoud El-Morshedy & Abd El-Moneim A. M. Teamah & Mohammed H. El-Menshawy & Rashad M. EL-Sagheer & Hasnaa M. Faied & Afrah Al-Bossly & Mohamed S. Eliwa, 2022. "Some Asymptotic Properties of a Kernel Bispectum Estimate with Different Multitapers," Mathematics, MDPI, vol. 10(18), pages 1-23, September.
    7. Hassler, U. & Marmol, F. & Velasco, C., 2006. "Residual log-periodogram inference for long-run relationships," Journal of Econometrics, Elsevier, vol. 130(1), pages 165-207, January.
    8. 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.
    9. Kokoszka, Piotr & Mikosch, Thomas, 2000. "The periodogram at the Fourier frequencies," Stochastic Processes and their Applications, Elsevier, vol. 86(1), pages 49-79, March.
    10. Chang Sik Kim & Peter C.B. Phillips, 2006. "Log Periodogram Regression: The Nonstationary Case," Cowles Foundation Discussion Papers 1587, Cowles Foundation for Research in Economics, Yale University.
    11. Haihan Yu & Mark S Kaiser & Daniel J Nordman, 2023. "A subsampling perspective for extending the validity of state-of-the-art bootstraps in the frequency domain," Biometrika, Biometrika Trust, vol. 110(4), pages 1099-1115.
    12. La Vecchia, Davide & Ronchetti, Elvezio, 2019. "Saddlepoint approximations for short and long memory time series: A frequency domain approach," Journal of Econometrics, Elsevier, vol. 213(2), pages 578-592.
    13. 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.
    14. Xiaofeng Shao, 2010. "Corrigendum: A self‐normalized approach to confidence interval construction in time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(5), pages 695-696, November.
    15. Proietti, Tommaso & Luati, Alessandra, 2015. "The generalised autocovariance function," Journal of Econometrics, Elsevier, vol. 186(1), pages 245-257.
    16. Kokoszka, P. & Mikosch, T., 1997. "The integrated periodogram for long-memory processes with finite or infinite variance," Stochastic Processes and their Applications, Elsevier, vol. 66(1), pages 55-78, February.
    17. Hernandez-Flores, C. N. & Artiles-Romero, J. & Saavedra-Santana, P., 1999. "Estimation of the population spectrum with replicated time series," Computational Statistics & Data Analysis, Elsevier, vol. 30(3), pages 271-280, May.
    18. Kun Chen & Ngai Hang Chan & Chun Yip Yau, 2020. "Bartlett correction of frequency domain empirical likelihood for time series with unknown innovation variance," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(5), pages 1159-1173, October.
    19. Rademacher, Daniel & Kreiß, Jens-Peter & Paparoditis, Efstathios, 2024. "Asymptotic normality of spectral means of Hilbert space valued random processes," Stochastic Processes and their Applications, Elsevier, vol. 173(C).
    20. Vetter, Mathias, 2014. "Inference on the Lévy measure in case of noisy observations," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 125-133.

    More about this item

    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:bla:jtsera:v:16:y:1995:i:6:p:585-606. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782 .

    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.