Mutual relevance of investor sentiment and finance by modeling coupled stochastic systems with MARS
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Mutual relevance of investor sentiment and finance by modeling coupled stochastic systems with MARS Betül Kalaycı1
· Ay¸se Özmen1 · Gerhard-Wilhelm Weber1,2
© Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract 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. Keywords Stochastic differential equations · Parameter estimation · Economics · Neurofinance · Behavioral finance · Investor sentiment · MARS
1 Introduction Dynamical processes in nature, economy and, especially, finance and cognitive sciences are exposed to random effects and noise. These time-dependent processes are generally characterized by their large number and by a high frequency. Since large datasets from financial
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Betül Kalaycı [email protected]
1
Institute of Applied Mathematics, Middle East Technical University, Ankara, Turkey
2
Faculty of Engineering Management and Economic Engineering, Poznan University of Technology, Pozna´n, Poland
123
Annals of Operations Research
observations and collective neural computations included in decision making and their behavioral outcomes have discretely discontinuous piecewise constant structures, expressing these high-frequency observations is a challenge (Kalaycı 2017; Jeanblanc et al. 2009). Therefore, to cope with these oscillations, a mathematical model has to be established. While composing such a model, high sensitivity with respect to oscillations and nonsmoothness of the data should be treated carefully (Kalaycı 2017; Taylan and Weber 2008; Weber et al. 2010). Our main purpose is to construct a coupled systems with the representation of SDEs in the sectors of finance, neurofinance
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