We investigate several aspects of GARCH(p,q) models which are relevant for empirical applications. In particular, we … note that the inclusion of a dummy variable as regressor can lead to multimodality in the GARCH likelihood. This makes … on the GARCH parameter space. We present a small refinement to the Nelson-Cao (1992) conditions for a GARCH(2,q) model …

highly dependent on the magnitude of shocks themselves. Markov-Switching GARCH (MS-GARCH) models are a valuable tool for … dynamics, it is here suggested to use a modification of the component GARCH model proposed by Ding and Granger (1996) in which … lagged values of the conditional standard deviation. Differently from MS-GARCH models, likelihood based inference for the …

univariate ARCH-type models including the GARCH, EGARCH, GJR, APARCH, IGARCH, FIGARCH, FIEGARCH and FIAPARCH specifications of …