Relationship between the benchmark interest rate and a macroeconomic indicator

A Poisson process with stochastic intensity is utilized to model changes of a benchmark interest rate set by a Central Bank. We propose explicit formulas for estimators of parameters and the expectation of the intensity, based on observations of the process. Through comparing the intensity and an economic indicator, we can explore the pattern of the benchmark interest rate. Two empirical datasets are studied and the results reveal similarities and differences between the behavior and the goals of Central Banks.