Long Memory Study Of Interval Financial Time Series

In the increasingly complex trend of financial markets,the "efficient market hypothesis" and "Random walk theory" are being challenged.Whether financial time series is long memory series and how to predict the financial time series with long memory has become research hotspots in recent years.However,there are several problems with the existing research on long memory of financial time series.Firstly,research objects are mostly sequences of point values,such as yield series or volatility sequence,and there is very few financial time series for interval type.Howe'ver,interval financial time series is widely existed in reality.Secondly,the method of testing long memory is too short to cover long memory characteristics,and the test results are not convincing.Finally,prediction models are mostly single models.They don't characterize the long memory characteristics of financial time series well so that the model is not accurate.Therefore,it is necessary to integrate the advantage of each model.In view of the existing problems,a test method for the long memory of interval financial time series and a long memory interval combination prediction model is proposed in this paper.The article includes two parts:testing the long memory of the interval financial time series is the first part.Firstly,the interval financial time series is divided into the interval center and the interval radius.Then,the long memory test is performed on the interval center series and the interval radius series by traditional long memory test methods.When both the interval center series and the interval radius series are long memory series,it indicates that this interval financial time series is long memory series.In the second part,a long memory interval combination prediction model is established for interval financial time series with long memory.The specific steps are as follows:firstly,the interval time series is rewritten into the interval center series and the interval radius series;then,several single prediction models of interval center series and interval radius series are established;finally,based on the prediction results of single models,the interval combination forecasting model with long memory is established.In order to verify the validity of the model,many domestic stock indexes were taken as the research objects in this paper,such as Shanghai Composite Index,Shenzhen Composite Index,Shanghai and Shenzhen 300 Index,Shenzhen 100 Index,Growth Enterprise Index and Sme board index.Firstly,the R/S method,the modified R/S method,DMA method,DFA method and GHE method were used to perform long memory test on these indexes.Then the test results were further tested for significance.The results show that the Shanghai Composite Index and the Shanghai and Shenzhen 300 Index are lo,ng memory financial time series,while the long memory characteristics of other financial time series are not obvious.Then,based on the Shanghai Composite Index and the Shanghai and Shenzhen 300 Index which have long memory,the interval combination prediction models of IOWGA operators about interval financial time series are established What's more,MSEP,MSEL,MSEI and MRIE are utilized to evaluate the accuracy and effectiveness of these models.Comparing with the definite prediction model,the combined prediction model can better exploit the advantages of each model and better characterize the long memory characteristics of interval financial time series.The contributions of this paper can be summarized in the following:Firstly,research objects are not point value series,but interval financial time series.Compared to the single point value series,the original interval series not only retains more information,but also uses more information when building the corresponding model;Secondly,the R/S method,the modified R/S method,DFA method,DMA method and GHE method are used to perform the long memory test on the interval financial time series.The same series is verified by five different detection methods in this paper in order to make the test results more convincing;Third,a mean model is established for the interval center series,and a volatility model is established for the interval radius series.Therefore,the final prediction results include both the mean information and the fluctuating information,and the information is more fully extracted;Fourth,combined forecasting model is used to forecast the interval centers series and interval radius series based on the consequences of various individual predictions.Combined forecasting model can combine the strength of each single forecasting method,and improves the prediction accuracy and effectiveness of the model.