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Bayesian mixture modeling for spectral density estimation

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  • Cadonna, Annalisa
  • Kottas, Athanasios
  • Prado, Raquel

Abstract

We develop a Bayesian modeling approach for spectral densities built from a local Gaussian mixture approximation to the Whittle log-likelihood. The implied model for the log-spectral density is a mixture of linear functions with frequency-dependent logistic weights, which allows for general shapes for smooth spectral densities. The proposed approach facilitates efficient posterior simulation as it casts the spectral density estimation problem in a mixture modeling framework for density estimation. The methodology is illustrated with synthetic and real data sets.

Suggested Citation

  • Cadonna, Annalisa & Kottas, Athanasios & Prado, Raquel, 2017. "Bayesian mixture modeling for spectral density estimation," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 189-195.
    • Handle: RePEc:eee:stapro:v:125:y:2017:i:c:p:189-195
    DOI: 10.1016/j.spl.2017.02.008
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    References listed on IDEAS

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    1. C. K. Carter & R. Kohn, 1997. "Semiparametric Bayesian Inference for Time Series with Mixed Spectra," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(1), pages 255-268.
    2. Ori Rosen & David S. Stoffer, 2007. "Automatic estimation of multivariate spectra via smoothing splines," Biometrika, Biometrika Trust, vol. 94(2), pages 335-345.
    3. Nicholas G. Polson & James G. Scott & Jesse Windle, 2013. "Bayesian Inference for Logistic Models Using Pólya--Gamma Latent Variables," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(504), pages 1339-1349, December.
    4. 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.
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    Cited by:

    1. 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).
    2. Patricio Maturana-Russel & Renate Meyer, 2021. "Bayesian spectral density estimation using P-splines with quantile-based knot placement," Computational Statistics, Springer, vol. 36(3), pages 2055-2077, September.
    3. 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).

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