Tweedie compound Poisson multivariate state space models for semicontinuous time series

Various approaches have been developed to analyze univariate semicontinuous time series data in the literature, whereas analysis of multivariate semicontinuous data has recently become an area of active research. However, there is apparently little, if any, literature on combining these two aspects to model multivariate semicontinuous time series data with covariates. In this paper, we introduce a family of multivariate state space models for semicontinuous time series data by incorporating serially correlated multivariate distribution-free random effects into Tweedie compound Poisson regression model. This model can flexibly accommodate unstructured covariance structures, skewness and zero-inflation. Unlike two-part modelling models, our model maintains natural temporal and multivariate structures of the data and characterizes the effects of covariates on the overall mean of the multivariate semicontinuous time series directly. An optimal estimation of our model has been developed using the orthodox best linear unbiased predictors of the serially correlated multivariate random effects. The usefulness of our approach is illustrated through the analysis of monthly national financing data in China and simulation studies.