On a vector double autoregressive model

Motivated by the double autoregressive (DAR) model, in this paper, we study a vector double autoregressive model (VDAR). The model is a straightforward extension from univariate case to multivariate case. Sufficient ergodicity conditions are given for the model. Without existence of second moment conditions for observed time series, the quasi maximum likelihood estimator (QMLE) of the parameter in the model is shown to be asymptotically normal, which does not hold for classic vector autoregressive (VAR) model with i.i.d errors. Simulation results confirm that our estimators perform well. A given empirical study implies the proposed model has potential applications in practice.