Parameter Estimation of Threshold OU Process

This study focuses on analyzing interest rate dynamics trends in different economies. First, we derive the marginal distribution of the threshold Ornstein-Uhlenbeck (OU) process. Then, we explicitly construct its probability density function (PDF). Additionally, we use the maximum likelihood estimation (MLE) method to estimate the model parameters, as it is statistically robust and ensures reliable results. Afterwards, we utilize historical interest rate data from four countries: China, the United States, the United Kingdom and Switzerland to validate the model parameter estimates. We've figured out that the threshold OU model is better at capturing the nonlinear dynamics in interest rates. Consequently, the model can furnish a reference basis for monetary policy formulation and financial decision-making in a variable macroeconomic environment.