An Analysis of Logarithmic Return Using Threshold Regression Based on the Ornstein–Uhlenbeck Process

In this paper, we introduce the threshold regression based on the Ornstein-Uhlenbeck (OU) process to capture the behavior of the logarithmic returns alternatively to the classical first hitting time model based on the Brownian motion. The model estimates the likelihood of the logarithmic returns reaching a threshold, thereby allowing us to interpret return risk through the first hitting time distribution. In our study, we assess the performance of the threshold regression based on the Ornstein-Uhlenbeck process comparing with threshold regression based on the Brownian motion (BM) model using different stock markets including the Stock Exchange of Thailand (SET), the Hong Kong Stock Exchange (HKSE), and the National Association of Securities Dealers Automated Quotations (NASDAQ). Empirical results indicate that the threshold regression model based on the Ornstein-Uhlenbeck process provides a better fit to the first hitting time of the logarithmic return and offers improved insight into the properties of returns upon reaching the threshold.