Likelihood Ratio Test for Detecting Change Points in the Exponentiated Exponential Logistic Distribution with Applications to Cryptocurrency Data

Detecting structural changes or change points in statistical models is a fundamental component of data analysis, as it plays a crucial role in understanding the dynamic behavior of real-world data, particularly in financial markets and cryptocurrency returns. In this study, we developed a procedure based on the likelihood ratio test (LRT) to identify change points in the parameters of the exponentiated exponential logistic (EEL) distribution. Furthermore, the binary segmentation technique was employed to efficiently detect multiple change points and determine their locations. The proposed methodology was derived under the null and alternative hypotheses, and its statistical properties were examined in depth. To evaluate its performance, extensive Monte Carlo simulations were conducted to assess the empirical power of the test under various sample sizes and significance levels. Furthermore, the method was applied to real cryptocurrency return data to demonstrate its practical ability to detect change points and illustrate its effectiveness at identifying structural breaks. The empirical results indicate that the LRT-based procedure exhibits strong capability in detecting significant distributional changes in cryptocurrency data over time, confirming its effectiveness as an analytical tool in statistical and financial studies.