Change-point Detection In The Skew Slash Distribution

The skew slash distribution is a ype of distribution with a skewed and heavy tail.It is mainly used for simulation research.In recent years,it has been widely used to fit and analyze data in the fields of finance,medicine,and meteorology.However,in real life,these data are often changed by some external factors,causing certain losses.For these fields,it is very important to analyze and detect changes in the data and make timely response strategies.Therefore,this paper studies the problem of change point detection with the skew slash distribution.The main research results are as follows:(1)Give the basic principles of maximum likelihood estimation and the EM algorithm,and use maximum likelihood estimation to estimate the parameters of the skew slash distribution proposed by Tian et al.in 2018.Because the log-likelihood function of the distribution is very complicated,it is impossible to directly solve the parameter equations,so this paper uses the fslove function in MATLAB software to assist in solving the estimated values of the parameters.The EM algorithm is used to estimate the parameters of the generalized hyperbolic skew slash distribution,which prepares the knowledge for the establishment of the change point detection model.(2)Based on the skew slash distribution proposed by Tian et al.in 2018,a log-likelihood ratio(LRT)change point detection model was established.The approximate value of empirical critical value under different significance levels and different sample sizes is obtained by 5000 times of Monte Carlo simulation.The pcrformancc of the established model in the detection of change-points is verified through simulation.Finally,the established LRT change point detection model is applied to the domestic and foreign stock market data,and the feasibility of the model is tested by finding the change point consistent with the actual historical changes.(3)The change-point detection model based on a more flexible generalized hyperbolic skew slash distribution is discussed.The log-likelihood ratio test(LRT),modified information criterion(MIC),and Bayesian information criterion(BIC)change-point detection models are established respectively.The effect of the three detection models to detect the change point was compared and analyzed through simulations,and it was found that for the same distribution,the performance of the MIC detection model to detect the change point was better than the other two detection models.Finally,the MIC change point detection model was applied to two domestic stock market data,and the detected change points were consistent with the actual historical changes,which verified the feasibility of the model.