Predictive and Structural Analysis for High-Dimensional Vector

This paper tackles the problem of estimating a high-dimensional vector autoregression (VAR). The estimation of these high-dimensional systems is done via regularization procedures that select the model and estimates the parameters simultaneously and is particularly useful in vector autoregressive context. This paper builds on the penalized least square procedures proposed by Nicholson et al. (2018). All procedures consist of penalty functions that are made up of hierarchically nested Euclidean norms of the model-coefficients. I augment these regularization models with a function that increases with the variables’ lag, incorporating the temporal dependence of the VAR more accurately. Moreover, I propose a new regularization model that is able to estimate high-dimensional VARs. The efficacy of the procedures, both in terms of forecasting and model discovery, is demonstrated in a simulation study as well as an empirical study. In addition, I show that high-dimensional VARs estimated by the proposed regularization methods produce credible impulse responses and are suitable for structural analysis.