Generalized Whittle likelihood for Bayesian nonparametric spectral density estimation
Date: 29 October 2020, Thursday
Time: 9am AEDT / 11am NZDT
Speaker: Prof Renate Meyer (The University of Auckland)
Abstract:
Most nonparametric Bayesian approaches use Whittle's likelihood to estimate the spectral density as the main nonparametric characteristic of stationary time series, as e.g. Choudhuri et al. (2004) and Rosen et al. (2012). However, the loss of efficiency of the nonparametric approach using Whittle's likelihood can be substantial. We show that the Whittle likelihood can be regarded as a special case of a nonparametrically corrected parametric likelihood which gives rise to a robust and more efficient Bayesian nonparametric spectral density estimate based on a generalized Whittle likelihood (Kirch et al. 2019). We prove that the posterior distribution based on the generalized Whittle likelihood and the nonparametric Bernstein-Dirichlet process prior is consistent for Gaussian stationary time series. An implementation is available in the R package "beyondWhittle". Frequentist properties are investigated in a simulation study and applications to LIGO gravitational wave data and the El Nino Southern Oscillation phenomenon will be described. We demonstrate that an extension to multivariate time series is possible using the Matrix Gamma process prior of Meier et al. (2020).
References:
Choudhuri, N., Ghosal, S., and Roy, A. (2004). Bayesian estimation of the spectraldensity of a time series. Journal of the American Statistical Association, 99(468): 1050–1059.
Kirch, C., Edwards, M. C., Meier, A., and Meyer, R. (2019). Beyond Whittle: Nonparametric Correction of a Parametric Likelihood with a Focus on Bayesian Time Series Analysis. Bayesian Analysis, 14, 1037-1073.
Rosen, O., Wood, S., Stoffer, D.S. (2012). AdaptSPEC: Adaptive Spectral Estimation for Nonstationary Time Series, Journal of the American Statistical Association, 107:500, 1575-1589.
Meier, A., Kirch, C., Edwards, M.C., Meyer, R. (2020). Bayesian Nonparametric Analysis of Multivariate Time Series: A Matrix Gamma Process Approach. Journal of Multivariate Analysis, 175 104560.
Time: 9am AEDT / 11am NZDT
Speaker: Prof Renate Meyer (The University of Auckland)
Abstract:
Most nonparametric Bayesian approaches use Whittle's likelihood to estimate the spectral density as the main nonparametric characteristic of stationary time series, as e.g. Choudhuri et al. (2004) and Rosen et al. (2012). However, the loss of efficiency of the nonparametric approach using Whittle's likelihood can be substantial. We show that the Whittle likelihood can be regarded as a special case of a nonparametrically corrected parametric likelihood which gives rise to a robust and more efficient Bayesian nonparametric spectral density estimate based on a generalized Whittle likelihood (Kirch et al. 2019). We prove that the posterior distribution based on the generalized Whittle likelihood and the nonparametric Bernstein-Dirichlet process prior is consistent for Gaussian stationary time series. An implementation is available in the R package "beyondWhittle". Frequentist properties are investigated in a simulation study and applications to LIGO gravitational wave data and the El Nino Southern Oscillation phenomenon will be described. We demonstrate that an extension to multivariate time series is possible using the Matrix Gamma process prior of Meier et al. (2020).
References:
Choudhuri, N., Ghosal, S., and Roy, A. (2004). Bayesian estimation of the spectraldensity of a time series. Journal of the American Statistical Association, 99(468): 1050–1059.
Kirch, C., Edwards, M. C., Meier, A., and Meyer, R. (2019). Beyond Whittle: Nonparametric Correction of a Parametric Likelihood with a Focus on Bayesian Time Series Analysis. Bayesian Analysis, 14, 1037-1073.
Rosen, O., Wood, S., Stoffer, D.S. (2012). AdaptSPEC: Adaptive Spectral Estimation for Nonstationary Time Series, Journal of the American Statistical Association, 107:500, 1575-1589.
Meier, A., Kirch, C., Edwards, M.C., Meyer, R. (2020). Bayesian Nonparametric Analysis of Multivariate Time Series: A Matrix Gamma Process Approach. Journal of Multivariate Analysis, 175 104560.
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