  Generative moment matching networks (GMMNs) are introduced as dependence
models for the joint innovation distribution of multivariate time series (MTS).
Following the popular copula-GARCH approach for modeling dependent MTS data, a
framework based on a GMMN-GARCH approach is presented. First, ARMA-GARCH models
are utilized to capture the serial dependence within each univariate marginal
time series. Second, if the number of marginal time series is large, principal
component analysis (PCA) is used as a dimension-reduction step. Last, the
remaining cross-sectional dependence is modeled via a GMMN, the main
contribution of this work. GMMNs are highly flexible and easy to simulate from,
which is a major advantage over the copula-GARCH approach. Applications
involving yield curve modeling and the analysis of foreign exchange-rate
returns demonstrate the utility of the GMMN-GARCH approach, especially in terms
of producing better empirical predictive distributions and making better
probabilistic forecasts.
