On a Partially Non-Stationary Vector AR Model with Vector GARCH Noises: Estimation and Testing

This paper studies a partially nonstationary vector autoregressive (VAR) model with vector GARCH noises. We study the full rank and the reduced rank quasi-maximum likelihood estimators (QMLE) of parameters in the model. It is shown that both QMLE of long-run parameters asymptotically converge to a functional of two correlated vector Brownian motions. Based these, the likelihood ratio (LR) test statistic for cointegration rank is shown to be a functional of the standard Brownian motion and normal vector, asymptotically. As far as we know, our test is new in the literature. The critical values of the LR test are simulated via the Monte Carlo method. The performance of this test in finite samples is examined through Monte Carlo experiments. We apply our approach to an empirical example of three interest rates.