Extracting Sparse and Ununiform Lag Structure Inherent in VAR Models with Latent Group Regularized Learning

Abstract

In multivariate time series data, it is important to capture time-delay structure where the necessary lag length to explain each variable is different. However, from the viewpoint of effectively using structurally regularized learning, when we apply conventional structurally regularized learning methods such as the Group LASSO, some problems, which include loss of necessary coefficients, occur. To overcome these problems, we propose a method based on the Latent Group LASSO regularization. To apply it to VAR models, we introduce overlapped coefficient groups in the time direction and use a heavy-tailed distribution, such as Student's $t$-distribution, as a prior to enhancing its sparsity. We evaluated the effectiveness of the proposed method using artificial data and actual data set (Beijing PM2.5 data set). As a result, we obtained the sparse models that capture the ununiform time-delay structure represented by fewer variables with the same degree of forecast accuracy comparing with ordinary VAR models.