10/20/16 | 4:15pm | E51-315
Reception to follow.
Abstract: Vector autoregression (VAR) is a fundamental tool for modeling multivariate time series. However, as the number of component series is increased, the VAR model becomes overparameterized. Several authors have addressed this issue by incorporating regularized approaches, such as the lasso in VAR estimation. Traditional approaches address overparameterization by selecting a low lag order, based on the assumption of short range dependence, assuming that a universal lag order applies to all components. Such an approach constrains the relationship between the components and impedes forecast performance. The lasso-based approaches work much better in high-dimensional situations but do not incorporate the notion of lag order selection. We propose a new class of regularized VAR models, called hierarchical vector autoregression (HVAR), that embed the notion of lag selection into a convex regularizer. The key modeling tool is a group lasso with nested groups which guarantees that the sparsity pattern of lag coefficients honors the VAR’s ordered structure. The HVAR framework offers three structures, which allow for varying levels of flexibility. A simulation study demonstrates improved performance in forecasting and lag order selection over previous approaches, and two macroeconomic applications further highlight forecasting improvements as well as HVAR’s convenient, interpretable output. Our manuscript is available here: http://arxiv.org/abs/1412.5250
Bio: David S. Matteson is an Assistant Professor of Statistical Science at Cornell University, where he is a member of the ILR School, Center for Applied Mathematics, Field of Operations Research, and the Program in Financial Engineering. His research interests include multivariate time series, signal processing, econometrics, spatio-temporal modeling, dimension reduction, machine learning, biostatistics, Bayesian analysis, nonparametrics, functional data, and many applications, including emergency medical services, biophysics, sustainable energy, neuroscience, finance and economics.