Copula models are widely employed in multivariate time series analysis because they permit flexible modelling of marginal distributions independently of the dependence structure, which is fully characterised by the copula function. However, Bayesian inference with these models becomes computationally demanding as the number of variables in the time series increases. Motivated by the classical inference functions for margins (IFM) approach, we propose a new neural-network based inference framework for estimating parameters in copula models, termed the neural inference functions for margins (N-IFM). N-IFM enables rapid parameter estimation for new data, fast sequential prediction, and efficient model comparison via time-series validation. We assess the performance of N-IFM using both simulated and real datasets and compare it to Hamiltonian Monte Carlo, demonstrating substantial computational gains with comparable inferential accuracy.

翻译：Copula模型广泛应用于多元时间序列分析，因其允许独立于完全由Copula函数表征的相关结构来灵活建模边际分布。然而，随着时间序列中变量数量的增加，这些模型的贝叶斯推断在计算上变得极具挑战性。受经典边际推断函数（IFM）方法的启发，我们提出了一种基于神经网络的新型推断框架，用于估计Copula模型参数，称为神经边际推断函数（N-IFM）。N-IFM能够实现新数据的快速参数估计、快速序列预测，并通过时间序列验证进行高效的模型比较。我们使用模拟数据集和真实数据集评估了N-IFM的性能，并将其与哈密顿蒙特卡洛方法进行了对比，结果表明在保持相当推断精度的前提下，N-IFM带来了显著的计算增益。