Optimal Test for Markov Switching GARCH Models

Empirically, the sum of GARCH parameter estimates is found to be close to unity, suggesting that the conditional volatility of most stock return data are likely to follow an integrated GARCH (IGARCH) process. However, such an extremely high persistence in unconditional variance may be overstated because of neglected structural breaks or parameter changes. As a result it is important to distinguish between these two processes, one being a globally stationary process and the other being a nonstationary IGARCH process. Though there are a number of studies modelling asymmetry leverage effects and advancing a battery of specification tests, studies that directly propose specification tests against Markov switching (MS) GARCH models are almost nonexistent. This paper develops such tests against MS-GARCH processes, which is shown to be asymptotically equivalent to the LR test. Furthermore, we consider the case in which the conditional variance follows an IGARCH process under the null whilst it is globally stationary under the alternative. Monte Carlo studies show that our proposed tests have a good finite sample performance. In an application to the weekly stock return data for five East Asian emerging markets, we find strong evidence in favor of MS-GARCH models.