Financial time series forecasting through neural stochastic differential equation

Details

Supervisors

Jungers, Raphaël M. ; Berger, Guillaume

Faculty

Ecole polytechnique de Louvain

Degree label

Master [120] : ingénieur civil en mathématiques appliquées, à finalité spécialisée

Abstract

enForecasting financial time series is a crucial yet challenging task due to their nonlinear characteristics and the presence of unpredictable jumps. To better anticipate market trends, it is essential to have tools capable of modeling these dynamics. In this context, neural stochastic models, such as LDE-Net, which leverage Lévy processes to capture jumps, have been developed. However, the standard use of this architecture has a significant theoretical limitation: the need for an appropriate loss function to accurately capture the underlying data dynamics. In this thesis, we explore a theoretically grounded approach by developing a novel loss function based on the log-likelihood of the α-stable distribution, computed via the Inverse Fourier Transform (IFT). We investigate how this new approach compares to benchmark models (ARIMA, LSTM) and existing stochastic variants, analyzing the results to determine whether it provides a more reliable and meaningful quantification of uncertainty.