  We consider a class of semi-parametric dynamic models with strong white noise
errors. This class of processes includes the standard Vector Autoregressive
(VAR) model, the nonfundamental structural VAR, the mixed causal-noncausal
models, as well as nonlinear dynamic models such as the (multivariate) ARCH-M
model. For estimation of processes in this class, we propose the Generalized
Covariance (GCov) estimator, which is obtained by minimizing a residual-based
multivariate portmanteau statistic as an alternative to the Generalized Method
of Moments. We derive the asymptotic properties of the GCov estimator and of
the associated residual-based portmanteau statistic. Moreover, we show that the
GCov estimators are semi-parametrically efficient and the residual-based
portmanteau statistics are asymptotically chi-square distributed. The finite
sample performance of the GCov estimator is illustrated in a simulation study.
The estimator is also applied to a dynamic model of cryptocurrency prices.
