# Copula Variational LSTM for High-dimensional Cross-market Multivariate Dependence Modeling

arXiv: https://arxiv.org/abs/2305.08778 · HTML: https://mlsanity.com/paper/2305.08778/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 85 references that are in the map.
- First posted on arXiv 9 May 2023.

## Builds on (most cited first, 16 of 16)

- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [A Recurrent Latent Variable Model for Sequential Data](https://mlsanity.com/paper/1506.02216/) (2015)
- [Spectral Temporal Graph Neural Network for Multivariate Time-series Forecasting](https://mlsanity.com/paper/2103.07719/) (2021)
- [Financial Time Series Forecasting with Deep Learning : A Systematic Literature Review: 2005-2019](https://mlsanity.com/paper/1911.13288/) (2019)
- [Neural Variational Inference for Text Processing](https://mlsanity.com/paper/1511.06038/) (2015)
- [Deep Learning for Financial Applications : A Survey](https://mlsanity.com/paper/2002.05786/) (2020)
- [AI in Finance: Challenges, Techniques and Opportunities](https://mlsanity.com/paper/2107.09051/) (2021)
- [Temporal Attention augmented Bilinear Network for Financial Time-Series Data Analysis](https://mlsanity.com/paper/1712.00975/) (2017)
- [Forecasting Economics and Financial Time Series: ARIMA vs. LSTM](https://mlsanity.com/paper/1803.06386/) (2018)
- [A Novel Ensemble Deep Learning Model for Stock Prediction Based on Stock Prices and News](https://mlsanity.com/paper/2007.12620/) (2020)
- [Coupling Learning of Complex Interactions](https://mlsanity.com/paper/2007.13534/) (2020)
- [Neural Gaussian Copula for Variational Autoencoder](https://mlsanity.com/paper/1909.03569/) (2019)
- [Gaussian Process Volatility Model](https://mlsanity.com/paper/1402.3085/) (2014)
- [Data science and AI in FinTech: An overview](https://mlsanity.com/paper/2007.12681/) (2020)
- [In-Depth Behavior Understanding and Use: The Behavior Informatics Approach](https://mlsanity.com/paper/2007.15516/) (2020)

## Built on by (most cited first, 2 of 2)

- [C2VAE: Gaussian Copula-based VAE Differing Disentangled from Coupled Representations with Contrastive Posterior](https://mlsanity.com/paper/2309.13303/) (2023)
- [A Copula-Guided Temporal Dependency Method for Multitemporal Hyperspectral Images Unmixing](https://mlsanity.com/paper/2509.11096/) (2025)

## Abstract (arXiv)

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.