Robust estimation of sparse vector autoregressive models

Abstract

This paper considers robust estimation of the sparse vector autoregressive model (sVAR) useful in highdimensional time series analysis.First, we generalize the result of Xu et al. (2008) that the adaptive lasso indeed has robustness in sVAR as well.However, adaptive lasso method in sVAR performs poorly as the number and sizes of outliers increases.Therefore, we propose new robust estimation methods for sVAR based on least absolute deviation (LAD) and Huber estimation.Our simulation results show that our proposed methods provide more accurate estimation in turn showed better forecasting performance when outliers exist.In addition, we applied our proposed methods to power usage data and confirmed that there are unignorable outliers and robust estimation taking such outliers into account improves forecasting.