Structured Regularization for Large Vector Autoregressions

• Activity Number: 460
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): William Nicholson*+ and Jacob Bien and David Scott Matteson
• Companies: Cornell University and Cornell University and Cornell University
• Keywords: Vector Autoregression ; Multivariate Time Series ; Regularization ; Lasso ; Group Lasso

Abstract

The vector autoregression (VAR) has long proven to be an effective method of macroeconomic forecasting, providing substantial improvements on univariate forecasts. One of the major disadvantages of the VAR that has hindered its applicability is that it is heavily parameterized. Unfortunately, this makes forecasting with VARs intractable for low-frequency, high-dimensional macroeconomic data. There is empirical evidence to suggest that VARs which incorporate many time series can result in more accurate forecasts than their smaller counterparts. By adapting regularization techniques to a time-series context, we seek to reduce the parameter space of VARs. We formulate convex optimization problems that are amenable to efficient solutions for the 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.