Discovering Sparse and Ununiform Lag Structure Using VAR Models with Latent Group LASSO Structurally regularized learning methods have been attracting attention in the field of statistics, machine learning, and signal processing as useful analysis tools for learning in highdimensional settings. Using these methods, specific structure can be represented in parameters. In multivariate time series data, it is important to capture timedelay structure where necessary lag length to explain each variable is different. In this paper, we deal with a problem to discover the optimal number of order for each variable in VAR models. When we apply conventional structurally regularized learning methods such as 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 time direction and use a heavytailed distribution, such as Studentu0027s tdistribution, as a prior to enhance its sparsity. We evaluated the effectiveness of the proposed method using artificial data and actual data set (Beijing PM2.5 data set). As the result, we obtained the sparse models that capture ununiform timedelay structure represented by fewer variables with the same degree of forecast accuracy comparing with ordinary VAR models.

Comparison of Variable Selection Methods for Forecasting from Short Time Series Forecasting from multivariate time series data is a difficult task, made more so in the situation where the number of series (p) is much larger than the length of each series (T), which makes dimension reduction desirable prior to obtaining a model. The LASSO has become a widelyused method to choose relevant covariates out of many candidates, and it has many variations and extensions, such as grouped LASSO, adaptive LASSO, weighted lag adaptive LASSO, and fused LASSO. Of these, only the weighted lag adaptive LASSO and the fused LASSO take into account natural ordering among series. To examine the ability of variations on the LASSO to choose relevant covariates for short time series we use simulations for series with fewer than 50 observations. We then apply the methods to a data set on significant changes in selfreported psychosocial symptoms in the 30 years after the Chornobyl nuclear catastrophe.