Parameter Estimation for Student's t VAR Model with Missing Data

Abstract

The vector autoregressive (VAR) models provide a significant tool for multivariate time series analysis. Most existing works on VAR modeling are based on 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. 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. Extensive experiments with synthetic data corroborate our claims.