Noncausal vector autoregressive process: Representation, identification and semi-parametric estimation

This paper introduces a representation theorem for a mixed VAR(p) process by distinguishing its causal and noncausal components. That representation is used to discuss the advantages and limitations of second-order identification in a mixed VAR. We show that it is possible to find the numbers of causal or noncausal components of the process from its multivariate autocovariance function, while nonlinear autocovariances are needed to distinguish between them. The paper introduces also a consistent semi-parametric estimator for mixed causal/noncausal multivariate non-Gaussian processes, called the Generalized Covariance (GCov) estimator, which relies on combined standard and nonlinear autocovariances of the process. The GCov does not require any distributional assumptions on the errors. The approach is illustrated by a simulation study and applied to commodity prices.