Using (GME) to Estimate kink Regression Models in Time Series (Applied Study)

This research aims to study the relationship between inflation and the general index of the stock market, using advanced statistical models capable of dealing with unstable time series with kink points. The time period was chosen from 2017 to 2024, where the data represents the dependent variable (the percentage change in the general index of the stock market) and the independent variable (the inflation rate). The studied data is characterized by instability, which makes traditional models ineffective to deal with it. Accordingly, the (kink regression) model was relied upon as an alternative that allows changing the marginal slope of the relationship before and after the kink point. In addition, a test was conducted for the models using different estimation methods, the first being the ordinary least squares method (OLS) and the second being the general maximum entropy method (GME). The study also included conducting a study of stability tests in order to determine the nature of the studied time series data and its stability. Among the most important of these tests is the Variance Ratio test and the Augmented Dickey-Fuller (ADF) test. The results of these tests proved that the data was suffering from instability and that it takes a random path. When using the Wald Test, the presence of a kink point was revealed and then the estimation was carried out, as the process of the estimation was conducted using two methods: the OLS method and the GME method.