# AdaptSPEC-X: Covariate Dependent Spectral Modeling of Multiple Nonstationary Time Series

## TL;DR

AdaptSPEC-X is a Bayesian covariate-dependent spectral model for analyzing multiple nonstationary time series, capable of handling missing data and estimating time-varying means and spectra with predictive capabilities.

## Contribution

It extends AdaptSPEC to incorporate covariates, handle missing data, and model time-varying means, enabling flexible joint analysis and prediction of nonstationary time series.

## Key findings

- Effective in simulated data
- Applied successfully to Australian rainfall data
- Demonstrated on US measles incidence

## Abstract

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 number of segments and estimates 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 model can estimate time varying means and spectra at 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. Software implementing the method proposed in this paper is available in the R package BayesSpec.