In this paper we introduce the STAR-STGARCH model that can characterize nonlinear behaviour both in the conditional mean and the conditional variance. A modelling cycle for this family of models, consisting of specification, estimation, and evaluation stages is constructed. Misspecification...

In this paper a unified framework for testing the adequacy of an estimated GARCH model is presented. Parametric LM or LM type tests of no ARCH in standardized errors, linearity, and parameter constancy are proposed. The asymptotic null distributions of the tests are standard, which makes...