Copula Variational LSTM for High-dimensional Cross-market Multivariate Dependence Modeling
Jia Xu, Longbing Cao IEEE Trans Neural Netw Learn Syst, 2023.
Access the paper at the arXiv website.

We address a challenging problem – modeling high-dimensional, long-range dependencies between non-normal multivariates, which is important for demanding applications like cross-market modeling (CMM). With heterogeneous indicators and markets, CMM aims to capture between-market financial couplings and influence over time and within-market interactions between financial variables. We make the first attempt to integrate deep variational sequential learning with copula-based statistical dependence modeling and characterize both temporal dependence degrees and structures between hidden variables representing non-normal multivariates. Our copula variational learning network WPVC-VLSTM integrates variational long short-term memory (LSTM) networks and regular vine copula to model variational sequential dependence degrees and structures. The regular vine copula models non-normal distributional dependence degrees and structures. VLSTM captures variational long-range dependencies coupling high-dimensional dynamic hidden variables without strong hypotheses and multivariate constraints. WPVC-VLSTM outperforms benchmarks including linear models, stochastic volatility models, deep neural networks, and variational recurrent networks in terms of both technical significance and portfolio forecasting performance. WPVC-VLSTM shows a step-forward for CMM and deep variational learning.