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 widely-used 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 self-reported psycho-social symptoms in the 30 years after the Chornobyl nuclear catastrophe.