We propose a multivariate GARCH model for non-stationary health time series by modifying the variance of the observations of the standard state space model. The proposed model provides an intuitive way of dealing with heteroskedastic data using the conditional nature of state space models. We follow the Bayesian paradigm to perform the inference procedure. In particular, we use Markov chain Monte Carlo methods to obtain samples from the resultant posterior distribution. Due to the natural temporal correlation structure induced on model parameters, we use the forward filtering backward sampling algorithm to efficiently obtain samples from the posterior distribution. The proposed model also handles missing data in a fully Bayesian fashion. We validate our model on synthetic data, and then use it to analyze a data set obtained from an intensive care unit in a Montreal hospital. We further show that our proposed models offer better performance, in terms of WAIC, than standard state space models. The proposed model provides a new way to model multivariate heteroskedastic non-stationary time series data and the simplicity in applying the WAIC allows us to compare competing models.

翻译：我们提出了一种针对非平稳健康时间序列数据的多元GARCH模型，该模型通过修改标准状态空间模型中观测值的方差来实现。所提出的模型利用状态空间模型的条件特性，为处理异方差数据提供了一种直观的方法。我们采用贝叶斯范式进行推断过程，具体而言，使用马尔可夫链蒙特卡洛方法从后验分布中获取样本。由于模型参数具有自然的时序相关结构，我们采用前向后向滤波采样算法高效地获取后验分布样本。该模型还以完全贝叶斯方式处理缺失数据。我们通过合成数据验证模型性能，随后将其用于分析蒙特利尔某医院重症监护室采集的数据集。进一步结果表明，在WAIC指标上，我们提出的模型优于标准状态空间模型。该模型为多元异方差非平稳时间序列数据建模提供了新方法，而WAIC的简便性使我们能够比较不同竞争模型。