| Abstract [eng] |
In recent decades, there has been a significant increase in the amount of data collected in various fields, such as nature, medicine, economics, and personal devices like smartwatches. Due to the vast and diverse nature of data, new techniques have emerged for data analysis. One of the problems often encountered in data analysis is structural changes in time series. A change point, also known as a structural break or regime shift is a point in time at which the mean, variance, pattern, distribution, or other statistical property in time series changes abruptly or continuously. In this dissertation, we aimed to develop a method for detecting change points in univariate and functional data samples. To this end, we proposed a mean instability testing model based on the p-variation of the process of partial sums and analysed its statistical power through simulation methods. We also established the limiting distribution for the null and alternative hypotheses theoretically. Furthermore, we generalized the results of the univariate test and applied them to functional data. In addition, we studied the asymptotic behaviour of the G-sums processes indexed by functions and established the limiting distribution theoretically. We proposed tests for detecting one change point, no more than m change points, and an unknown number of change points, and analysed these tests using simulation methods as well as real data. |
