Threshold regression based on geometric Brownian motion with application to stock market prices

The threshold regression model, first introduced by Lee and Whitmore in 2006 by combining the concepts of the first hitting time model and linear regression, has been widely applied in the medical context. The model features enhanced capabilities in incorporating information from auxiliary variables to model the target variable. These advances are evident not only in the medical context, but also in finance. Therefore, in this study, we extend the concept of the threshold regression model to financial data focusing on stock market prices. We construct a threshold regression model based on geometric Brownian motion, the conventional underlying process for the first hitting time models in financial data. We demonstrate advantages of the proposed model via applications to the stock exchange of Thailand (SET) compared with three reference models including the first hitting time model based on Brownian motion, the first hitting time model based on geometric Brownian motion, and the threshold regression model based on Brownian motion. Moreover, we enhance the quality of the proposed model by adapting a mixture cure fraction to the model. The results indicate that the proposed threshold regression based on geometric Brownian motion with a cure fraction outperforms other competing models.