Bayesian inference on periodicities and component spectral structure in time series (Q2703242)

Recent work on time series decomposition has stressed the utility of exploring estimated autoregressive models, among others, through inferred latent components of the time series under study. In this paper new classes of smoothness priors introduced recently by the authors [J. R. Stat. Soc., Ser. B 61, No. 4, 881-899 (1999; Zbl 0940.62079)] in developing Bayesian spectral inference are explored and exploited. The authors had an inferential focus on questions about model order and the effects of model order uncertainty on time series decompositions and other inferences. The current paper, in contrast, is concerned with the use of these models and priors in exploring the spectral composition of time series, and spectral density estimation.NEWLINENEWLINENEWLINEApplications to analysis of the frequency composition of time series, in both time and spectral domains, is illustrated in a study of a time series from astronomy. This analysis demonstrates the impact and utility of the new class of priors in addressing model order uncertainty and in allowing for unit root structure. Time-domain decomposition of a time series into estimated latent components provides an important alternative view of the component spectral characteristics of a series. In addition, the data analysis in this paper illustrates the utility of the smoothness prior and allowance for unit root structure in inference about spectral densities. In particular, the framework overcomes supposed problems in spectral estimation with autoregressive models using more traditional model-fitting methods.