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Title: AdaptSPEC-X: Covariate dependent spectral modeling of multiple nonstationary time series Authors:  Michael Bertolacci - University of Wollongong (Australia)
Ori Rosen - University of Texas at El Paso (United States)
Edward Cripps - The University of Western Australia (Australia)
Sally Cripps - University of Sydney (Australia) [presenting]
Abstract: A method for the joint analysis of a panel of possibly nonstationary time series is presented. The approach is Bayesian and uses a covariate-dependent infinite mixture model to incorporate multiple time series, with mixture components parameterized by a time-varying mean and log spectrum. The mixture components are based on AdaptSPEC, a nonparametric model which adaptively divides the time series into an unknown but nite number of segments and estimate the local log spectra by smoothing splines. We extend AdaptSPEC to handle missing values, a common feature of time series which can cause difficulties for nonparametric spectral methods. A second extension is to allow for a time-varying mean. Covariates, assumed to be time-independent, are incorporated via the mixture weights using the logistic stick-breaking process. The resulting model can estimate time-varying means and spectra at both observed and unobserved covariate values, allowing for predictive inference. Estimation is performed by Markov chain Monte Carlo (MCMC) methods, combining data augmentation, reversible jump, and Riemann manifold Hamiltonian Monte Carlo techniques. We evaluate the methodology using simulated data and describe applications to Australian rainfall data and measles incidence in the US. Efficient software implementing the proposed method is available in the R package BayesSpec.