Analysis Of The Influencing Factors Of The Stock Price Index Under The Mixture Cure Model

In recent years,censored data are increasingly common in survival analysis,and studies on interval-censored data are increasing.Interval-censored data occur when the specific time of the event is unknown and we only know whether the event occurs within an observation interval.In the research,there are some individuals who will never experience the event we are interested in for their own reasons or some special reasons.In other words,individuals who are immune to this event are called cured individuals.For interval-censored data with a cure part,the mixture cure model can be used for analysis.In this paper,we regard the time interval when the stock becomes a member of Shanghai stock exchange 50 index(SSE 50 index)for the first time as interval-censored data with a cure part.The specific time when the stock is eligible to enter SSE 50 index is unknown,only the time interval is known,which conforms to the definition of interval-censored data.However,due to the limitation of the number of constituent stocks of SSE 50 index,most stocks may never enter SSE 50 index,so we have reason to believe that there are cured individuals in the stock data.Based on the above background,this paper studies the problems of interval-censored data under the additive risk mixture cure model.Firstly,we summarize domestic and foreign research status of interval-censored data,the additive risk model,the mixture cure model and SSE 50 index.Secondly,we present the definition of survival time,the maximum likelihood estimation and Bernstein polynomials.Thirdly,we present the expression corresponding to the additive risk mixture cure model and derive the corresponding likelihood function.However,due to the parameters to be estimated contain an infinite-dimensional nonparametric component,regression analysis of interval-censored data under the additive risk model can be challenging in the maximation of the likelihood function.To solve this problem,we propose the sieve maximum likelihood estimation method based on Bernstein polynomials and evaluate the finite sample performance of the method by simulation studies.Finally,we apply the proposed method to the analysis of the influencing factors of the stock price index.We collect the time interval data and corresponding covariates data for the first time the stock becomes a member of SSE 50 index,and plot the Turnbull estimation curve of the sample survival function,which proves the existence of the cure part.We select covariates with the AIC criterion,then fit the additive risk mixture cure model,and indicate that the factors affecting stock survival time including exchange rate,reserve ratio,interest rate,the type of enterprise,the way of stock offering,net asset value per share and net interest rate of total assets.