An exact discretization of continuous time stochastic volatility processes observed at irregularly spaced times is used to give insights on how a coherent GARCH model can be specified for such data. The relation of our approach with those in the existing literature is studied

This paper derives the asymptotic distribution for a number of rank-based and classical residual specification tests in AR-GARCH type models. We consider tests for the null hypotheses of no linear and quadratic serial residual autocorrelation, residual symmetry, and no structural breaks. For...