A flexible two-piece normal dynamic linear model

We construct a flexible dynamic linear model for the analysis and prediction of multivariate time series, assuming a two-piece normal initial distribution for the state vector. We derive a novel Kalman filter for this model, obtaining a two components mixture as predictive and filtering distributions. In order to estimate the covariance of the error sequences, we develop a Gibbs-sampling algorithm to perform Bayesian inference. The proposed approach is validated and compared with a Gaussian dynamic linear model in simulations and on a real data set.