A dynamic linear model with extended skew-normal for the initial distribution of the state parameter

We develop a Bayesian dynamic model for modeling and forecasting multivariate time series relaxing the assumption of normality for the initial distribution of the state space parameter, and replacing it by a more flexible class of distributions, which we call Generalized Skew-Normal (GSN) Distributions. We develop a version of the classic Kalman filter, again obtaining GSN predictive and filtering distributions. As we are supposing the random fluctuations covariances to be unknown, a Gibbs-type sampler algorithm is developed in order to perform Bayesian inference. We work with two simulation experiments with scenarios close to real problems in order to show the efficacy of our proposed model. Finally, we apply our technique to a real data set.