MaxEnt-Fin: computational maximum entropy approach to high-dimensional modeling and analysis in finance

MaxEnt-Fin：金融领域高维建模和分析的计算最大熵方法

• 批准号: 529738942
• 负责人: Professor Dr. Illia Horenko
• 金额: --
• 依托单位: Facoltà di Scienze Economiche
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/529738942?language=en
• 关键词: MaxEnt; Fin; computational; maximum; entropy

Modeling and prediction of fluctuations (volatilities) in financial time series are among the core challenges in Economics and Finance. In the last several years, the accumulation of massive amounts of high-dimensional financial data was accompanied by an impressive development of econometric and machine learning (ML) approaches for the analysis of these data. Besides offering new exciting opportunities, recent applications of the emerging tools to the financial data has revealed some new methodological challenges related to the scalability, sensitivity, and comparability of the algorithms - as well as with respect to the interpretability of the obtained results and the study of the mathematical and statistical properties. For example, time series of stock returns are characterized by relatively few serial observations T (ranging from a few hundred observations with monthly data to a few thousands with daily data) and by many dimensions n (up to tens or hundreds of thousands, where n corresponds to different companies, but also to characteristics of those companies). Application of popular computational numerical tools from econometrics and machine learning to such “small T, large n” data generally aims at finding increasingly-elaborate models with many parameters that have to be tuned to few high-dimensional observations available. This can lead to a problem known as “overfitting”, i.e. the good quality of fit on the training data is combined with the poor predictive performance of the tuned models. Another limitation is imposed by the computational cost of the common numerical tools, increasing polynomially with the data dimension n. In this research proposal, we will develop numerical tools based on combining the recently-introduced Scalable Probabilistic Approximation (SPA) methods for adaptive data discretization with the Maximum Entropy principle from physics and information theory. Maximum Entropy principle (MaxEnt) aims at finding as simple as possible (but not simpler than necessary) models fitting the data, being least biased in terms of the underlying assumptions and minimal in terms of the total number of tunable parameters. We will develop a numerical discretization-driven MaxEnt framework for time series analysis and inference of latent cross-sectional interdependencies between different financial time series (like asset returns and credit ratings), allowing for computational uncertainty quantification and risk predictions based on time series from Economics and Finance.

金融时间序列波动的建模和预测是经济学和金融学的核心挑战之一。在过去的几年里，大量高维金融数据的积累伴随着计量经济学和机器学习（ML）方法的发展，这些方法用于分析这些数据。除了提供新的令人兴奋的机会，最近的应用程序的新兴工具的财务数据揭示了一些新的方法学的挑战，有关的可扩展性，灵敏度和算法的可比性-以及相对于所获得的结果的可解释性和研究的数学和统计属性。例如，股票收益的时间序列的特征在于相对较少的连续观测值T（从每月数据的几百个观测值到每天数据的几千个观测值）和许多维度n（高达数万或数十万，其中n对应于不同的公司，但也对应于这些公司的特征）。从计量经济学和机器学习到这种“小T，大n”数据的流行计算数值工具的应用通常旨在找到越来越复杂的模型，这些模型具有许多参数，必须调整到很少的高维观测值。这可能会导致一个被称为“过拟合”的问题，即训练数据上的良好拟合质量与调优模型的不良预测性能相结合。另一个限制是由普通数值工具的计算成本所施加的，其随着数据维度n而多项式地增加。在这项研究中，我们将开发数值工具的基础上结合最近推出的可扩展概率近似（SPA）方法，用于自适应数据离散化与物理学和信息论的最大熵原理。最大熵原理（MaxEnt）旨在找到尽可能简单（但不简单于必要）的模型来拟合数据，在基本假设方面偏差最小，在可调参数的总数方面最小。我们将开发一个数值离散化驱动的MaxEnt框架，用于时间序列分析和推断不同金融时间序列（如资产回报和信用评级）之间潜在的横截面相互依赖关系，允许基于经济学和金融学的时间序列进行计算不确定性量化和风险预测。