Lin Deng

Lin Deng, Michael Stanley Smith, Worapree Maneesoonthorn

Skew-t copula models are attractive for the modeling of financial data because they allow for asymmetric and extreme tail dependence. We show that the copula implicit in the skew-t distribution of Azzalini and Capitanio (2003) allows for a higher level of pairwise asymmetric dependence than two popular alternative skew-t copulas. Estimation of this copula in high dimensions is challenging, and we propose a fast and accurate Bayesian variational inference (VI) approach to do so. The method uses a generative representation of the skew-t distribution to define an augmented posterior that can be approximated accurately. A stochastic gradient ascent algorithm is used to solve the variational optimization. The methodology is used to estimate skew-t factor copula models with up to 15 factors for intraday returns from 2017 to 2021 on 93 U.S. equities. The copula captures substantial heterogeneity in asymmetric dependence over equity pairs, in addition to the variability in pairwise correlations. In a moving window study we show that the asymmetric dependencies also vary over time, and that intraday predictive densities from the skew-t copula are more accurate than those from benchmark copula models. Portfolio selection strategies based on the estimated pairwise asymmetric dependencies improve performance relative to the index.

Fuhang Liang, Rucong Xu, Deng Lin

Current deep regression models usually learn in a point-wise way that treats each sample as an independent input, neglecting the relative ordering among different data. Consequently, the regression model could neglect the data's interrelationships, potentially resulting in suboptimal performance. Moreover, the existence of aleatoric uncertainty in the training data may drive the model to capture non-generalizable patterns, contributing to increased overfitting. To address these issues, we propose a novel adaptive pairwise learning framework for regression tasks (AdaPRL) which leverages the relative differences between data points and integrates with deep probabilistic models to quantify the uncertainty associated with the predictions. Additionally, we adapt AdaPRL for applications in multi-task learning and multivariate time series forecasting. Extensive experiments with several real-world regression datasets including recommendation systems, age prediction, time series forecasting, natural language understanding, finance, and industry datasets show that AdaPRL is compatible with different backbone networks in various tasks and achieves state-of-the-art performance on the vast majority of tasks without extra inference cost, highlighting its notable potential including enhancing prediction accuracy and ranking ability, increasing generalization capability, improving robustness to noisy data, improving resilience to reduced data, and enhancing interpretability. Experiments also show that AdaPRL can be seamlessly incorporated into recently proposed regression frameworks to gain performance improvement.