Least Absolute Deviation Estimation for Uncertain Vector Autoregressive Model with Imprecise Data

Abstract

The uncertain vector autoregressive model is able to model the interrelationships between different variables, which is more advantageous compared to the traditional autoregressive model, when modeling real-life objects and where the observed values are imprecise. In this paper, the parameters of the uncertain vector autoregressive model are estimated by using least absolute deviation estimation (LAD) to obtain a fitted uncertain vector autoregressive model, and residual analysis is performed to obtain estimates of expected values and variances of the residuals. In addition, future values are modeled by using forecasting methods, i.e., point estimation and interval estimation. The order of the uncertain vector autoregressive model is also determined by the indicator summation of test errors (STE) in the cross-validation, and we also analyze that the least absolute deviation estimation outperforms the least squares estimation method in the presence of outliers.