Robust Estimation of Multivariate Time Series Data Based on Reduced Rank Model

Multivariate time series analysis uncovers the intricate relationships among multiple variables, which plays a vital role in areas such as policy-making and business decision-making. This paper employs a reduced rank regression model to investigate a robust estimation method for multivariate time series data using an ${\ell }_1$ penalty. The goal is to achieve rapid parameter estimation while ensuring robustness in the analysis of time series data. This study provides a detailed description of the solution process and examines the theoretical properties of the proposed method. To evaluate its effectiveness, the proposed model is compared with full-rank regression and the multivariate regression with covariance estimation (MRCE) method through simulations, as well as an analysis of the Sceaux household electric power consumption data. The results indicate that the proposed model performs well.