Multivariate time-series modeling with generative neural networks

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.