Estimation and inference of the vector autoregressive process under heteroscedasticity

In this paper we derive the asymptotic distribution of the estimator for the parameters of the vector autoregressive process of order p with an unconditionally heteroscedastic error process. The covariance matrix of the error process is modeled as a deterministic matrix function and it is estimated nonparametrically at each time point. This estimator is used for deriving inference procedures for the parameters of the vector autoregressive process.