Artificial regression testing in the GARCH - in - mean model

The issue of finite-sample inference in GARCH-like models has seldom been explored in the theoretical literature, although its potential relevance for practitioners is self-evident. In some cases, asymptotic theory may provide a very poor approximation to the actual distribution of the estimators in finite samples. The aim of this paper is to propose the application of the socalled double length regressions (DLR) to GARCH-in-mean models for inferential purposes. As an example, we focus on the issue of Lagrange Multiplier tests on the risk premium parameter. Simulation evidence suggests that DLR-based LM test statistics provides a much better testing framework than OPG-based LM test statistics, which is commonly used, in terms of actual test size, especially when the GARCH process exhibits high persistence in volatility. This result is consistent with previous studies on the subject.