Shrinkage Estimation of Linear Regression Models with GARCH Errors

Abstract

This paper introduces shrinkage estimators for the parameter vector of a linear regression model with conditionally heteroscedastic errors such as the class of generalized autoregressive conditional heteroscedastic (GARCH) errors when some of the regression parameters are restricted to a subspace. We derive the asymp-totic distributional biases and risks of the shrinkage estimators using a large sample theory. We show that if the shrinkage dimension exceeds two, the relative efficiency of the shrinkage estimator is strictly greater than that of the full model estimator. Furthermore, a Monte Carlo simulation study is conducted to examine the relative performance of the shrinkage estimators with the full model estimator. Our large sample theory and simulation study show that the shrinkage estimators dominate the full model estimator in the entire parameter space. We illustrate the proposed method using a real data set from econometrics.