A zero intercept Vec model

This paper introduces a multivariate volatility model that is characterized by nonstationarity irrespective of the parameters. The model is motivated by the multivariate GARCH model in VEC form, setting the intercept term to zero. We first discuss the conditions required for a positive definite conditional variance matrix. For the special case of a diagonal parameter matrix, we derive the conditions for stability of trajectories, meaning that the processes do not diverge to infinity or to zero almost surely. We then develop the asymptotic theory for maximum likelihood estimation, and propose a test of the null hypothesis of a zero Lyapunov exponent, i.e. stability. In a simulation study we demonstrate the good performance of the estimator and the test in finite samples.