AdaptSPEC-X: Covariate Dependent Spectral Modeling of Multiple Nonstationary Time Series
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We present a method for the joint analysis of a panel of possibly nonstationary time series. 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 finite number of segments and estimates the local log spectra by smoothing splines. We extend AdaptSPEC to handle multiple time series with time varying mean and missing values. 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 method proposed in this paper is available in the R package BayesSpec.
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