Specification Tests for Asymmetric GARCH

In this paper I present two new Lagrange multiplier test statistics designed for testing the null of GARCH (1,1), against the alternative of asymmetric GARCH. For one test the alternative is the generalized QARCH (1,1) model of Sentana [1995], and for the other the alternative is the logistic smooth transition GARCH (1,1) model of Hagerud [1996], and González-Rivera [1996]. In the study I present small sample properties for the two statistics. The empirical size is shown to be equal to the theoretical for reasonable sample sizes. Furthermore, I show that the power of both tests is superior to that of the asymmetry tests proposed by Engle and Ng [1993]. This is true even if the true data generating process is not the GQARCH or LSTGARCH model, but any of the models, EGARCH, GJR, TGARCH, A-PARCH, and VS-ARCH. Thus, the two tests are in fact tests for general GARCH asymmetry,.