Large Vector Auto Regressions

Abstract

One popular approach for nonstructural economic and nancial forecasting is to include a large number of economic and nancial variables, which has been shown to lead to signicant improvements for forecasting, for example, by the dynamic factor models. A challenging issue is to determine which variables and (their) lags are relevant, especially when there is a mixture of serial correlation (temporal dynamics), high dimensional (spatial) dependence structure and moderate sample size (relative to dimensionality and lags). To this end, an integrated solution that addresses these three challenges simultaneously is appealing. We study the large vector auto regressions here with three types of estimates. We treat each variable’s own lags dierent from other variables’ lags, distinguish various lags over time, and is able to select the variables and lags simultaneously. We rst show the consequences of using Lasso type estimate directly for time series without considering the temporal dependence. In contrast, our proposed method can