On testing the changes in trends of stock market index and rates

Calibration of interest rate models benefits from grouping data to homogenous classes. Such an approach is typical in many financial time series. Preliminaries have been developed for Cox–Ingersoll–Ross models but this issue remains an open problem for many more realistic interest rate models. Here we develop such a strategy for general class interest rate and classes are based on p-value thresholds for testing for normality and gamma distributions. We use as the benchmark financial series of Chilean stock market index IPSA (Indice de precios selectivo de acciones) and its log-returns. We also study the relationship between interest rate and the market returns represented by the IPSA indicator, with positive correlation in some lags which reveals some interesting facts in the contrary to the conventional theory.