Student'S T Var Modeling With Missing Data Via Stochastic Em And Gibbs Sampling

The vector autoregressive (VAR) models provide a significant tool for multivariate time series analysis. Owing to the mathematical simplicity, existing works on VAR modeling are rigidly inclined towards the multivariate Gaussian distribution. However, heavy-tailed distributions are suggested more reasonable for capturing the real-world phenomena, like the presence of outliers and a stronger possibility of extreme values. Furthermore, missing values in observed data is a real problem, which typically happens during the data observation or recording process. Although there exist numerous works on VAR modeling with heavy-tailed distributions, they assume the availability of complete data and are not applicable in the presence of missing data. In this paper, we propose an algorithmic framework to estimate the parameters of a VAR model with heavy-tailed Student' s t distributed innovations from incomplete data based on the stochastic approximation expectation maximization (SAEM) algorithm coupled with a Markov Chain Monte Carlo (MCMC) procedure. We propose two fast and computationally cheap Gibbs sampling schemes, both based on MCMC procedure. The algorithms developed are effective in capturing the heavy-tailed phenomenon and being robust against outliers and missing data. In addition, owing to their low computational complexity, the algorithms are amenable for highdimensional and big data applications. Extensive experiments with both synthetic data and real financial data corroborate our claims.