Asymmetric vector moving average models: Estimation and testing

We propose the class of asymmetric vector moving average (asVMA) models.
The asymmetry of these models is characterized by different MA filters applied to the components of vectors of lagged positive and negative innovations. This allows for a detailed investigation of the interrelationships among past model innovations of different sign. We derive some covariance matrix properties of an asVMA model under the assumption of Gaussianity. Related to this, we investigate the global invertibility condition of the proposed model. The paper also introduces a maximum likelihood estimation procedure and a multivariate Wald-type test statistic for symmetry versus the alternative of asymmetry. The finite-sample performance of the proposed multivariate test is studied by simulation. Furthermore, we devise an exploratory test statistic based on lagged sample cross-bicovariance estimates. The estimation and testing procedures are used to uncover asymmetric effects in two US growth rates, and in three US industrial prices.