Estimating and Forecasting Multivariate Autoregressive Time Series Models Using Goal Programming

Abstract

 This paper presents a new method for estimation and prediction of vector autoregressive (VAR) models by goal programming (GP). VAR models have been widely used in economics, finance, and engineering, but most of the times they are estimated and forecasted using least squares or maximum likelihood estimation, which are sensitive to non-normality, outlier, and small samples. The proposed GP is a re-formulation of the estimation of VAR models as an optimization problem, where the absolute difference is minimized to enhance the robustness. Validation of the methodology is carried out through a large Monte Carlo simulation study based on 108 scenarios, and the real world application with economic series data for USA and environmental and climate science data for China. Results show that GP has more forecasting accuracy and robustness than comparison methods (ordinary least squares (OLS), Bayesian var, M- estimator), especially when contaminated and outlier conditions arise. This study is also a contribution to the literature as it is the first to use GP to solve a multivariate time series problem, which offers a flexible and reliable tool for researchers and practitioners who face problems in data-driven decision making.