Bayesian parametric, nonparametric and semiparametric procedures for spectral density inference of univariate and multivariate time series
The package contains several methods (parametric, nonparametric and semiparametric) for Bayesian spectral density inference. The main algorithms to fit the models for univariate time series are:
gibbs_ar: Parametric, autoregressive (AR) model
gibbs_np: Nonparametric model with Whittle's likelihood and Bernstein-Dirichlet prior from Choudhuri et al (2007)
gibbs_npc: Semiparametric model with corrected AR likelihood and Bernstein-Dirichlet prior from Kirch et al (2018)
The package also contains the following models for multivariate time series:
gibbs_var: Parametric, vector autoregressive (VAR) model
gibbs_vnp: Nonparametric model with Whittle's likelihood and Bernstein-Hpd-Gamma prior from Meier (2018)
as well as some useful utility functions. To get started, it is recommended to consider the examples and documentation of the functions listed above. The work was supported by DFG grant KI 1443/3-1.
N. Choudhuri, S. Ghosal and A. Roy (2004) Bayesian estimation of the spectral density of a time series JASA <doi:10.1198/016214504000000557>
C. Kirch, M. C. Edwards, A. Meier and R. Meyer (2018) Beyond Whittle: Nonparametric Correction of a Parametric Likelihood with a Focus on Bayesian Time Series Analysis Bayesian Analysis <doi:10.1214/18-BA1126>
A. Meier (2018) A matrix Gamma process and applications to Bayesian analysis of multivariate time series PhD thesis, OvGU Magdeburg <doi:10.25673/13407>