DETECTING FOR SMOOTH STRUCTURAL CHANGES IN GARCH MODELS

Detecting and modeling structural changes in GARCH processes have attracted increasing attention in time series econometrics. In this paper, we propose a new approach to testing structural changes in GARCH models. The idea is to compare the log likelihood of a time-varying parameter GARCH model with that of a constant parameter GARCH model, where the time-varying GARCH parameters are estimated by a local quasi-maximum likelihood estimator (QMLE) and the constant GARCH parameters are estimated by a standard QMLE. The test does not require any prior information about the alternatives of structural changes. It has an asymptotic N(0,1) distribution under the null hypothesis of parameter constancy and is consistent against a vast class of smooth structural changes as well as abrupt structural breaks with possibly unknown break points. A consistent parametric bootstrap is employed to provide a reliable inference in finite samples and a simulation study highlights the merits of our test.