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 allowing us to take an alternative 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, our main contribution. 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 are presented to demonstrate the utility of our approach, especially in terms of producing better empirical predictive distributions and making better probabilistic forecasts. All results are reproducible with the demo GMMN_MTS_paper of the R package gnn.