Abstract: This paper introduces a new class of bivariate time series models, Cross-Related Structural Models (CRSMs). In this class of models, each time series is modeled by a structural time series model and the structural parameters are modeled as functions of the latent history of the other series. These models preserve certain conditional independence structures over time and can incorporate all the features of the univariate state space models. With minimum modifications, existing forecasting and filtering algorithms for the univariate models can be applied to these models. By modeling the cross relationships through the structural parameters, these models allow flexible relationships to be modeled parsimoniously and include parameters with clear interpretations. An application to a bivariate hormone time series with pulses is used as an illustration.
Key words and phrases: Conditionally Gaussian model, multivariate time series model, multiprocess dynamic linear model, pulsatile time series, state space model.