Research And Empirical Analysis Of The Construction Of China's Investor Sentiment Index Based On The Optimal Filtering Method

With the appearance of a large number of financial anomalies and irrational behaviors,traditional financial theory failed to make reasonable explanations.Scholars have begun to explain financial anomalies from a new perspective,and gradually formed a behavioral financial theory.Investor sentiment theory is one of the important branches of behavioral finance,and the measurement of investor sentiment are always one of the difficulty problems in the study of behavioral finance.The research on the relationship between investor sentiment and stock returns is also the hot spot of behavioral finance.This paper studies the construction of investor sentiment index and its impact on stock market returns.It has important practical reference significance for investors to invest in stock market decision-making and relevant regulatory agencies.The theoretical significance of this paper lies in the integration of the optimal filtering method into the financial research,constructing the investor sentiment index by filtering method,and deeply researching the investor sentiment theory,which can be used as a reference for the development of investor sentiment theory.In this paper,for the selection of investor sentiment indicators,four representative proxy variables are selected from a number of emotional representative variables.These include variables such as the number of newly added investors,the turnover rate,the first day IPO yield,and the closed-end fund discount rate.In the data processing of IPO first day return rate and closed-end fund discount rate,this paper adopts boxplot method with skew degree adjustment to remove outliers and compare other methods for removing outliers.In order to make the sample data continuous in time and expand the sample range,a cubic spline interpolation method was used to supplement a large amount of missing data.Compared with other methods in the literature,new ideas are proposed for reference.The method in this paper has certain guiding significance.Firstly,this paper studies the method of constructing investor sentiment index,using Kalman filter based on EM algorithm,extended Kalman filter based on EM algorithm and particle filter respectively to construct investor sentiment index.In order to test the reasonable validity of the emotional index constructed by the three methods,a robust principal component analysis method was used to construct an investor sentiment index,and the four sentiment indexes were tested for correlation.Comparison of the accuracy of the sentiment index by the root mean square error,and the irrational investor sentiment index was obtained by removing the influence of relevant macroeconomic factors.Secondly,this paper studies the relationship between the irrational investor sentiment index and the return rate of the Shanghai Stock Exchange Index,and establishes VAR model,Granger test,VAR model parameter estimation and impulse response analysis.An empirical analysis of the yield of the Shanghai Composite Index and an in-depth study of the relationship between investor sentiment and stock returns.The results of the study show that the investor sentiment index constructed by different methods is slightly different,but there is a high correlation between the four investor sentiment indexes,and the sentiment index is roughly the same.Therefore,Kalman filtering based on EM algorithm,extended Kalman filtering based on EM algorithm and particle filtering can be used to construct investor sentiment index,which has certain robustness.According to the RMSE analysis,the investor sentiment index constructed by particle filter has the highest accuracy.Through Granger's test,there is a significant Granger influence between the irrational principal component sentiment index and the Shanghai Stock Index's return rate,which is a Granger causality and can interact with each other.The non-rational Kalman filter sentiment index,irrational extended Kalman filter sentiment index,and irrational particle filter sentiment index could not produce Granger effect on the yield of the Shanghai index,and only the one-way effect of the return of the Shanghai index on investor sentiment.Because of Granger causality between stock returns and irrational investor sentiment,a VAR model can be established.Through VAR model parameter estimation,the study considers that in the long-term phase,there are significant inverse relations between the four irrational investor sentiments and stock returns.The irrational investor sentiment counteracts the returns of the Shanghai Stock Index and can predict changes in future stock returns.And the irrational investor sentiment index has higher first-order autocorrelation.Through impulse response analysis,in the short term,a positive change in stock returns will lead to an increase in irrational investor sentiment,and a negative change in stock returns will lead to a drop in irrational investor sentiment,but then maintain optimism.In the short term,pessimistic investor sentiment changes will strongly cause a negative reaction to stock returns.There is a positive relationship between the yield of the Shanghai index and the four irrational investor sentiment indexes.