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We propose a multivariate GARCH model for non-stationary health time seriesby modifying the variance of the observations of the standard state spacemodel. The proposed model provides an intuitive way of dealing withheteroskedastic data using the conditional nature of state space models. Wefollow the Bayesian paradigm to perform the inference procedure. In particular,we use Markov chain Monte Carlo methods to obtain samples from the resultantposterior distribution. Due to the natural temporal correlation structureinduced on model parameters, we use the forward filtering backward samplingalgorithm to efficiently obtain samples from the posterior distribution. Theproposed model also handles missing data in a fully Bayesian fashion. Wevalidate our model on synthetic data, and then use it to analyze a data setobtained from an intensive care unit in a Montreal hospital. We further showthat our proposed models offer better performance, in terms of WAIC, thanstandard state space models. The proposed model provides a new way to modelmultivariate heteroskedastic non-stationary time series data and the simplicityin applying the WAIC allows us to compare competing models.

A Bayesian Non-Stationary Heteroskedastic Time Series Model for Multivariate Critical Care Data