IDEAS home Printed from https://ideas.repec.org/a/oup/biomet/v100y2013i2p447-458.html
   My bibliography  Save this article

Penalized multivariate Whittle likelihood for power spectrum estimation

Author

Listed:
  • Robert T. Krafty
  • William O. Collinge

Abstract

Nonparametric estimation procedures that can flexibly account for varying levels of smoothness among different functional parameters, such as penalized likelihoods, have been developed in a variety of settings. However, geometric constraints on power spectra have limited the development of such methods when estimating the power spectrum of a vector-valued time series. This article introduces a penalized likelihood approach to nonparametric multivariate spectral analysis through the minimization of a penalized Whittle negative loglikelihood. This likelihood is derived from the large-sample distribution of the periodogram and includes a penalty function that forms a measure of regularity on multivariate power spectra. The approach allows for varying levels of smoothness among spectral components while accounting for the positive definiteness of spectral matrices and the Hermitian and periodic structures of power spectra as functions of frequency. The consistency of the proposed estimator is derived and its empirical performance is demonstrated in a simulation study and in an analysis of indoor air quality. Copyright 2013, Oxford University Press.

Suggested Citation

  • Robert T. Krafty & William O. Collinge, 2013. "Penalized multivariate Whittle likelihood for power spectrum estimation," Biometrika, Biometrika Trust, vol. 100(2), pages 447-458.
  • Handle: RePEc:oup:biomet:v:100:y:2013:i:2:p:447-458
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1093/biomet/ass088
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. von Sachs, Rainer, 2019. "Spectral Analysis of Multivariate Time Series," LIDAM Discussion Papers ISBA 2019008, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Chau, Van Vinh & von Sachs, Rainer, 2017. "Positive-Definite Multivariate Spectral Estimation: A Geometric Wavelet Approach," LIDAM Discussion Papers ISBA 2017002, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Hu, Zhixiong & Prado, Raquel, 2023. "Fast Bayesian inference on spectral analysis of multivariate stationary time series," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    4. Robert T. Krafty & Ori Rosen & David S. Stoffer & Daniel J. Buysse & Martica H. Hall, 2017. "Conditional Spectral Analysis of Replicated Multiple Time Series With Application to Nocturnal Physiology," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1405-1416, October.
    5. Granados-Garcia, Guilllermo & Fiecas, Mark & Babak, Shahbaba & Fortin, Norbert J. & Ombao, Hernando, 2022. "Brain waves analysis via a non-parametric Bayesian mixture of autoregressive kernels," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    6. Fiecas, Mark & von Sachs, Rainer, 2013. "Data-driven Shrinkage of the Spectral Density Matrix of a High-dimensional Time Series," LIDAM Discussion Papers ISBA 2013044, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. Shibin Zhang, 2022. "Automatic estimation of spatial spectra via smoothing splines," Computational Statistics, Springer, vol. 37(2), pages 565-590, April.
    8. Robert T. Krafty & Haoyi Fu & Jessica L. Graves & Scott A. Bruce & Martica H. Hall & Stephen F. Smagula, 2019. "Measuring Variability in Rest-Activity Rhythms from Actigraphy with Application to Characterizing Symptoms of Depression," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 11(2), pages 314-333, July.
    9. Zhang, Shibin, 2019. "Bayesian copula spectral analysis for stationary time series," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 166-179.
    10. Zhang, Shibin, 2016. "Adaptive spectral estimation for nonstationary multivariate time series," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 330-349.
    11. Robert T. Krafty, 2016. "Discriminant Analysis of Time Series in the Presence of Within-Group Spectral Variability," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(4), pages 435-450, July.
    12. 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.

    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:oup:biomet:v:100:y:2013:i:2:p:447-458. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Oxford University Press (email available below). General contact details of provider: https://academic.oup.com/biomet .

    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.