| Structure change analysis,which can establish functional relations between variables in economic system and explain its relevant meaning,is one of the most important problems in economic system modeling.A large number of empirical studies show that futures market has the function of price discovery,and futures price is the leading indicator of spot price.Therefore,it is of practical significance to study the relationship between futures and spot market.The traditional cointegration model can only simply depict the long-term equilibrium relationship between futures and spot,while cointegration model with structural changes can also find out the structural change information between futures and spot.In the time series,a structural change point is called time series change point,which mainly includes the mean change point and the variance change point.In this paper,structural change points of China stock market stock index and stock index futures is studied by judging the basis sequence.If basis is changed before and after one moment,then we get the position of structural change point.This problem belongs to the change point problem,so this paper is also analyzed the relationship between futures and spot in China securities market by combining three methods for the detection of change point and cointegration model with structural changes.The research object of this paper is Shanghai 50 Futures Price Index and its spot price index.We choose the daily closing price sequence of Shanghai 50 Futures Price Index and its spot price index from April 16,2015 to September 1,2017 as the research samples.Using three kinds of time series change point detection method to find structural change point position in the basis sequence,establish cointegration model with structural changes between Shanghai 50 Futures Price Index and its spot price index.The results show that:(1)Granger causality test and the impulse response analysis are done for the Shanghai 50 Futures and its spot price.The test results show that the Shanghai 50 index of futures price is ahead of the Shanghai 50 stock price index,and impulse response analysis shows that the impact of a current Shanghai 50 Futures price change will bring the same impact to the spot price.This reflects the futures are ahead of the spot,which has the function of price discovery.(2)In the detection of change point of spread sequence mean,three time series change point detection method are used,which are the least square method,maximum likelihood ratio detection method and mean variance based on the analysis of a change point detection method.Least squares detection and maximum likelihood ratio detection are common detection methods,and the method of mean change point detection based on one-way variance analysis is proposed in this paper.The experimental simulation shows that the mean change point detection method based on the one-way variance analysis is also effective,which is compared with the traditional least square detection and the maximum likelihood ratio detection.The structural changes point is only one by using three kinds of time series change point detection means in the sequence of Shanghai 50 basis points.(3)Through E-G cointegration and Johansen cointegration test,there is a cointegration relationship between Shanghai 50 Futures and its stock market.This cointegration relationship shows that the Shanghai 50 Futures price is positively correlated with its spot price,and the correlation is high,which satisfies the long-term equilibrium relationship.Using structural change point of the basis sequence to establish cointegration model with structural changes between Shanghai 50 Futures Price Index and its spot price index,the fitting effect of the optimal model is the state switch integration model.From the model expression,we know that the impact of Shanghai 50 Futures Price on its spot price is positive,and the positive impact of Shanghai 50 Futures Price on its spot price is stronger after the change point. |
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