RR-FiME-11-08 Nazim Regnard This paper establishes the asymptotic properties of the quasi-maximum likelihood estimator (QMLE) of a GARCH(1,1) process with time-varying cofficients driven by an exogenous variable, when some true coefficients may be null. The QMLE is shown to be consistent. Its asymptotic distribution is a projection of a normal vector distribution onto a convex cone. Furthermore, the QMLE is shown to converge to its asymptotic distribution locally uniformly. We then consider the Read more [...]