Structured Regularization for Large Vector Autoregression

The vector autoregression (VAR), has long proven to be an effective method for modeling the joint dynamics of macroeconomic time series as well as forecasting. One of the major disadvantages of the VAR that has hindered its applicability is its heavy parameterization; the parameter space grows quadratically with the number of series included, quickly exhausting the available degrees of freedom. Consequently, forecasting using VARs is intractable for low-frequency, high dimensional macroeconomic data. However, empirical evidence suggests that VARs which incorporate more component series tend to result in more accurate forecasts than their smaller counterparts. Existing methods which allow for the estimation of large VARs either tend to require ad-hoc specifications or are computationally intractable. We adapt several prominent scalar regression regularization techniques to a vector time series context to greatly reduce the parameter space of VARs. We formulate convex optimization procedures that are amenable to efficient solutions for the time ordered high-dimensional problems we aim to solve. Through this framework, we propose a structured family of models and provide implementations which allow for both the efficient estimation and accurate forecasting of high-dimensional VARs. We demonstrate their efficacy in simulated data examples as well as an application to a large set of macroeconomic indicators. ∗PhD Student, Department of Statistical Science, Cornell University, 301 Malott Hall, Ithaca, NY 14853 (E-mail: [email protected]; Webpage: http://www.wbnicholson.com) †Assistant Professor, Department of Statistical Science and Department of Social Statistics, Cornell University, 1196 Comstock Hall, Ithaca, NY 14853, (E-mail: [email protected]; Webpage: https://courses.cit.cornell. edu/~dm484/) ‡Assistant Professor, Department of Biological Statistics and Computational Biology and Department of Statistical Science, Cornell University, 1178 Comstock Hall, Ithaca, NY 14853 (E-mail: [email protected]; Webpage: http://faculty.bscb.cornell.edu/~bien/)