Stein combination shrinkage for vector autoregressions
|Speaker:||Bruce E. Hansen, University of Wisconsin-Madison|
|Date: ||Friday 19 May 2017|
|Location: ||Matrix Lecture Theatre, Building One|
This paper introduces Stein combination shrinkage for vector autoregressions (VARs). The proposed methods shrink unrestricted least-squares VAR estimates towards multiple user-specified linear constraints, including lag exclusion and autoregressive models. We propose weighted combination estimators, where the weights minimize an estimate of the mean-squared error (MSE) of a vector-valued parameter of interest. Particular attention is given to impulse response estimation and multi-period point forecasting. The combination estimators are similar to Stein shrinkage estimators. Our proposed weights are specific to the horizon, which allows the degree of shrinkage to adapt across horizons. The proposed methods are evaluated in a careful simulation experiment. The simulation evidence shows that the Stein combination methods have much lower MSE than conventional OLS and BVAR methods. We illustrate the methods with an application to a standard seven-variable system of U.S. macroeconomic aggregates.