Copula Variational LSTM for High-dimensional Cross-market Multivariate
  Dependence Modeling
Jia Xu Longbing Cao
We address an important yet challenging problem - modeling high-dimensional
dependencies across multivariates such as financial indicators in heterogeneous
markets. In reality, a market couples and influences others over time, and the
financial variables of a market are also coupled. We make the first attempt to
integrate variational sequential neural learning with copula-based dependence
modeling to characterize both temporal observable and latent variable-based
dependence degrees and structures across non-normal multivariates. Our
variational neural network WPVC-VLSTM models variational sequential dependence
degrees and structures across multivariate time series by variational long
short-term memory networks and regular vine copula. The regular vine copula
models nonnormal and long-range distributional couplings across multiple
dynamic variables. WPVC-VLSTM is verified in terms of both technical
significance and portfolio forecasting performance. It outperforms benchmarks
including linear models, stochastic volatility models, deep neural networks,
and variational recurrent networks in cross-market portfolio forecasting.