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

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 fewthousands 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. The research work is structured in three complementary research directions (subprojects) and will be performed by the two PIs, one PostDoc, and two Ph.D. students. (Subproject I) Sparse extension of nonstationary MaxEnt methods from one to multiple dimensions and numerical analysis of the methodology (estimation of computational scalability, sensitivity, and convergence properties). (Subproject II) Development and numerical analysis of discrete MaxEnt methods for scalable and simultaneous entropy maximization, feature selection, anddiscretization for high-dimensional “small T, large n” data. (Subproject III) Development and numerical analysis of scalable methods for “small T, large n” transfer learning from econometrics time series - i.e., when transforming the time series to images (e.g., to scalograms) and combining the Deep Learning (DL) network pretrained on “big” image data (e.g., GoogleNet) for feature extraction with MaxEnt and discretization tools from Subprojects I and II. The scientific results will be the content of several research papers to be submitted to top journals in Econometrics, Computational Science, and mathematical foundations of ML methodology. The questions investigated and the methods developed in this project are important both for their topical relevance in the academic community and for the practical implications in the management of financial risks.