IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v151y2020ics0167947320301109.html
   My bibliography  Save this article

Nonparametric Bayesian inference for the spectral density based on irregularly spaced data

Author

Listed:
  • Zhang, Shibin

Abstract

Various approaches for spectral analysis based on regularly spaced data have already been well-established, but the spectral inference based on irregularly spaced data are still essentially limited. Under the Bayesian framework, a detouring approach for spectral estimation is proposed for analyzing irregularly spaced data. The detouring process is accomplished by three steps: (1) normalizing the data in some sense on frequency domain by a time-scale change, (2) estimating the spectral density of the time-scale changed process, and (3) solving the estimated spectrum by the relation of spectral densities between the model and its time-scale-changed version. The proposed approach uses a Hamiltonian Monte Carlo—within Gibbs technique to fit smoothing splines to the periodogram. Our technique produces an automatically smoothed spectral estimate. The time-scale-change not only allows basis functions in the smoothing splines to be independent of sampling design, but also makes the proposed estimation need not to adjust tuning parameters according to different irregularly spaced data.

Suggested Citation

  • Zhang, Shibin, 2020. "Nonparametric Bayesian inference for the spectral density based on irregularly spaced data," Computational Statistics & Data Analysis, Elsevier, vol. 151(C).
    • Handle: RePEc:eee:csdana:v:151:y:2020:i:c:s0167947320301109
    DOI: 10.1016/j.csda.2020.107019
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947320301109
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2020.107019?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
    ---><---

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

    References listed on IDEAS

    as
    1. Rosen, Ori & Stoffer, David S. & Wood, Sally, 2009. "Local Spectral Analysis via a Bayesian Mixture of Smoothing Splines," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 249-262.
    2. Zeda Li & Robert T. Krafty, 2019. "Adaptive Bayesian Time–Frequency Analysis of Multivariate Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(525), pages 453-465, January.
    3. Ori Rosen & David S. Stoffer, 2007. "Automatic estimation of multivariate spectra via smoothing splines," Biometrika, Biometrika Trust, vol. 94(2), pages 335-345.
    4. Mark Fiecas & Hernando Ombao, 2016. "Modeling the Evolution of Dynamic Brain Processes During an Associative Learning Experiment," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1440-1453, October.
    5. Ombao H. C & Raz J. A & von Sachs R. & Malow B. A, 2001. "Automatic Statistical Analysis of Bivariate Nonstationary Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 543-560, June.
    6. Zhang, Shibin, 2016. "Adaptive spectral estimation for nonstationary multivariate time series," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 330-349.
    7. 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.
    8. Yasumasa Matsuda & Yoshihiro Yajima, 2009. "Fourier analysis of irregularly spaced data on Rd," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 191-217, January.
    9. Nidhan Choudhuri & Subhashis Ghosal & Anindya Roy, 2004. "Bayesian Estimation of the Spectral Density of a Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1050-1059, December.
    10. Sally A. Wood, 2002. "Bayesian mixture of splines for spatially adaptive nonparametric regression," Biometrika, Biometrika Trust, vol. 89(3), pages 513-528, August.
    11. Shibin Zhang & Xin M. Tu, 2018. "Tests for Comparing Time‐Invariant and Time‐Varying Spectra Based on the Pearson Statistic," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(5), pages 709-730, September.
    12. Scott A. Bruce & Martica H. Hall & Daniel J. Buysse & Robert T. Krafty, 2018. "Conditional adaptive Bayesian spectral analysis of nonstationary biomedical time series," Biometrics, The International Biometric Society, vol. 74(1), pages 260-269, March.
    13. Ori Rosen & Sally Wood & David S. Stoffer, 2012. "AdaptSPEC: Adaptive Spectral Estimation for Nonstationary Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1575-1589, December.
    14. Zhang, Shibin, 2019. "Bayesian copula spectral analysis for stationary time series," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 166-179.
    15. Wang, Zhu, 2013. "cts: An R Package for Continuous Time Autoregressive Models via Kalman Filter," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 53(i05).
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Shibin Zhang, 2022. "Automatic estimation of spatial spectra via smoothing splines," Computational Statistics, Springer, vol. 37(2), pages 565-590, April.

    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. Shibin Zhang, 2022. "Automatic estimation of spatial spectra via smoothing splines," Computational Statistics, Springer, vol. 37(2), pages 565-590, April.
    2. Hu, Zhixiong & Prado, Raquel, 2023. "Fast Bayesian inference on spectral analysis of multivariate stationary time series," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    3. Zhang, Shibin, 2019. "Bayesian copula spectral analysis for stationary time series," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 166-179.
    4. 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).
    5. Zhang, Shibin, 2016. "Adaptive spectral estimation for nonstationary multivariate time series," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 330-349.
    6. 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.
    7. Brian Hart & Michele Guindani & Stephen Malone & Mark Fiecas, 2022. "A nonparametric Bayesian model for estimating spectral densities of resting‐state EEG twin data," Biometrics, The International Biometric Society, vol. 78(1), pages 313-323, March.
    8. Chau, Joris & von Sachs, Rainer, 2022. "Time-varying spectral matrix estimation via intrinsic wavelet regression for surfaces of Hermitian positive definite matrices," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    9. Meier, Alexander & Kirch, Claudia & Meyer, Renate, 2020. "Bayesian nonparametric analysis of multivariate time series: A matrix Gamma Process approach," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    10. Yakun Wang & Zeda Li & Scott A. Bruce, 2023. "Adaptive Bayesian sum of trees model for covariate‐dependent spectral analysis," Biometrics, The International Biometric Society, vol. 79(3), pages 1826-1839, September.
    11. Ori Rosen & Sally Wood & David S. Stoffer, 2012. "AdaptSPEC: Adaptive Spectral Estimation for Nonstationary Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1575-1589, December.
    12. Christian Macaro & Raquel Prado, 2014. "Spectral Decompositions of Multiple Time Series: A Bayesian Non-parametric Approach," Psychometrika, Springer;The Psychometric Society, vol. 79(1), pages 105-129, January.
    13. Chau, Van Vinh & von Sachs, Rainer, 2018. "Intrinsic wavelet regression for surfaces of Hermitian positive definite matrices," LIDAM Discussion Papers ISBA 2018025, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    14. Mark Fiecas & Hernando Ombao, 2016. "Modeling the Evolution of Dynamic Brain Processes During an Associative Learning Experiment," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1440-1453, October.
    15. Fontaine, Charles & Frostig, Ron D. & Ombao, Hernando, 2020. "Modeling non-linear spectral domain dependence using copulas with applications to rat local field potentials," Econometrics and Statistics, Elsevier, vol. 15(C), pages 85-103.
    16. Tommaso Proietti & Alessandra Luati, 2013. "The Exponential Model for the Spectrum of a Time Series: Extensions and Applications," CEIS Research Paper 272, Tor Vergata University, CEIS, revised 19 Apr 2013.
    17. 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).
    18. Scott A. Bruce & Martica H. Hall & Daniel J. Buysse & Robert T. Krafty, 2018. "Conditional adaptive Bayesian spectral analysis of nonstationary biomedical time series," Biometrics, The International Biometric Society, vol. 74(1), pages 260-269, March.
    19. Boland, Joanna & Telesca, Donatello & Sugar, Catherine & Jeste, Shafali & Goldbeck, Cameron & Senturk, Damla, 2022. "A study of longitudinal trends in time-frequency transformations of EEG data during a learning experiment," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    20. Davide Pigoli & Pantelis Z. Hadjipantelis & John S. Coleman & John A. D. Aston, 2018. "The statistical analysis of acoustic phonetic data: exploring differences between spoken Romance languages," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 67(5), pages 1103-1145, November.

    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:eee:csdana:v:151:y:2020:i:c:s0167947320301109. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.