用神经贝叶斯方法快速估计莱维过程参数,计算效率高且结果可靠。
Fast Likelihood-Free Parameter Estimation for Lévy Processes
- 基于置换不变神经网络的模拟推断框架,无需显式似然函数
- 在多个莱维模型上优于传统方法,准确率更高、耗时更短
- 适合高频金融数据建模,尤其适用于比特币等加密资产长期分析
莱维过程因其能捕捉高频资产收益率中的间断与重尾特性,广泛用于金融建模。然而,当似然函数不可用或计算成本过高时,参数估计仍具挑战性。本文提出一种基于神经贝叶斯估计(NBE)框架的快速准确方法,该方法为基于模拟的无似然推断技术,利用置换不变神经网络近似贝叶斯估计器。我们给出了新的理论结果,证明在温和条件下NBE可得一致估计,其风险收敛至贝叶斯估计量。通过多种莱维模型的大量模拟实验,表明NBE在准确性和运行时间上均优于传统方法,并支持两种互补的不确定性量化方式。我们在一个具有挑战性的高频加密货币收益率数据集上验证了该方法,成功捕捉参数动态变化,在远低于传统方法的计算成本下实现可靠且可解释的推断。该方法可在数秒内完成一整年数据的参数估计,对近十年比特币高频回报数据的处理也仅需不到一分钟。
原文摘要 · Abstract (English)
Lévy processes are widely used in financial modeling due to their ability to capture discontinuities and heavy tails, which are common in high-frequency asset return data. However, parameter estimation remains a challenge when associated likelihoods are unavailable or costly to compute. We propose a fast and accurate method for Lévy parameter estimation using the neural Bayes estimation (NBE) framework -- a simulation-based, likelihood-free approach that leverages permutation-invariant neural networks to approximate Bayes estimators. We contribute new theoretical results, showing that NBE results in consistent estimators whose risk converges to the Bayes estimator under mild conditions. Moreover, through extensive simulations across several Lévy models, we show that NBE outperforms traditional methods in both accuracy and runtime, while also enabling two complementary approaches to uncertainty quantification. We illustrate our approach on a challenging high-frequency cryptocurrency return dataset, where the method captures evolving parameter dynamics and delivers reliable and interpretable inference at a fraction of the computational cost of traditional methods. NBE provides a scalable and practical solution for inference in complex financial models, enabling parameter estimation and uncertainty quantification over an entire year of data in just seconds. We additionally investigate nearly a decade of high-frequency Bitcoin returns, requiring less than one minute to estimate parameters under the proposed approach.
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