Modeling And Empirical Analysis Of Dependent High-Frequency Financial Data Based On Semi-Markov Chains

This article employs a model framework that combines a semi-Markov chain with Copula functions to study the volatility and correlation of high-frequency asset returns.High-frequency asset return sequences exhibit characteristics such as volatility clusters and nonlinear correlations,requiring more flexible and accurate modeling methods to characterize volatility and correlation.Semi-Markov chains allow the waiting time series for state transitions to follow any distribution,which can better describe the process of return state transitions,so this article uses a semi-Markov chain to describe the volatility of a single financial asset return.Since financial asset returns are often not isolated,but are interconnected,Copula functions can construct joint distributions directly without linear transformations,accurately capturing nonlinear correlations.Therefore,this article uses Copula functions to describe the correlations between high-frequency financial asset return sequences.This article conducts empirical analysis using the return rate data of six highfrequency indices in the C SI 300 Index.First,a semi-Markov model is established for the returns of the six indices,and it is found that most of the indices are in a stable return state,with the probability of transferring to a stable return state being the highest at the next moment when extreme fluctuations occur.Then,the correlation between the returns of the six indices is studied.Based on the waiting time series of index return state transitions,a Copula model is constructed to explore the correlation between the returns of the main consumption index and the returns of other indices.It is found that there is a high correlation between the return of the main consumption index and the return of other indices,and different Copula functions need to be used to measure the correlation between the return of the main consumption index and the return of other indices.AIC and BIC criteria are used to select Copula functions,and empirical research shows that the static SJC Copula,dynamic SJC Copula,and t-Copula perform better than other Copula functions.Through data analysis,it is found that the main consumption index is the economic foundation,and changes in the return of the main consumption index will cause changes in the return of other indices.During the period of economic growth,there is a strong correlation between the main consumption index return rate and the industrial index return rate and bank index return rate at the end.The rise in the main consumption index return rate can cause an increase in the industrial index return rate and bank index return rate.However,during an economic downturn,there is a strong negative correlation between the main consumption index return rate and the return rates of the other five indices.A decrease in the main consumption index return rate will lead to a decrease in the return rates of the other five indices.In conclusion,by fitting asset return volatility with a semi-Markov model and using Copula functions to capture the correlation between high-frequency financial asset returns,financial risk can be assessed and managed more accurately.