Mutual relevance of investor sentiment and finance by modeling coupled stochastic systems with MARS

Stochastic differential equations (SDEs) rapidly become one of the most well-known formats in which to express such diverse mathematical models under uncertainty such as financial models, neural systems, behavioral and neural responses, human reactions and behaviors. They belong to the main methods to describe randomness of a dynamical model today. In a financial system, different kinds of SDEs have been elaborated to model various financial assets. On the other hand, economists have conducted research on several empirical phenomena regarding the behaviour of individual investors, such as how their emotions and opinions influence their decisions. All those emotions and opinions are described by the word Sentiment. In finance, stochastic changes might occur according to investors' sentiment levels. In our study, we aim to represent the mutual effects between some financial process and investors' sentiment with constructing a coupled system of non-autonomous SDEs, evolving in time. These equations are hard to assess and solve. Therefore, we express them in a simplified manner by discretization and Multivariate Adaptive Regression Splines (MARS) model. MARS is a strong method for flexible regression and classification with interactive variables. Hereby, we treat time as another spatial variable. Eventually, we present a modern application with real-world data. This study finishes with a conclusion and an outlook towards future studies.