Statistical Inference Of Time Series Quantile Regression Model Based On EM Algorithm

Stock prices can reflect a country’s economic situation,and stock market fluctuations can also have an impact on investors’ behavior.Currently,with the rapid development of China’s economy,the uncertainty and risks of the economic market are constantly highlighted.Traditional methods based on linear correlation coefficient analysis are no longer suitable for research on the stock market,and time series models are also receiving increasing attention.Quantile regression can not only relax model assumptions,but also describe the performance of data at different quantiles,so it becomes one of the preferred models for robust statistical analysis.In this paper,EM algorithm is mainly used to estimate the quantile regression model of time series data.First,quantile estimation is made for the double autoregressive model,and then Bayesian variable selection is made for the quantile regression model of autoregressive error.In the first part of this paper,we introduce the quantile estimation based on EM algorithm under the double autoregressive model,and redefine the model by introducing the mixture of asymmetric Laplacian distributions.On the basis of quasi likelihood,the EM algorithm is applied to the model solving process to obtain parameter estimates at different quantiles.Simulation studies have found that the mean square error in estimating non zero true values in parameters is very small,and as the sample size increases,the mean square error decreases,resulting in better estimation results;And select the model order through the BIC criterion,with accurate results and high accuracy.In empirical analysis,prediction research was conducted on the stock price data of the Shanghai and Shenzhen300 Index,verifying the superiority of this model in studying stock data.In the second part of the article,Bayesian variables are selected for the quantile regression model with autoregressive error based on the EM algorithm.Considering the quantile regression model with autoregressive error,the mixture of asymmetric Laplacian distribution is introduced to rewrite the model.The problem of Bayesian variable selection is studied under the quasi likelihood framework.Spike and slab prior and 0-1 latent variables are constructed,the full condition distribution is given,and the EM algorithm is used to select Bayesian variables.In the simulation study,four different error distributions were studied to compare the differences in the impact of different errors on parameter estimation and variable selection.Finally,empirical analysis was conducted on the data of the New York Stock Exchange Composite Index to study the factors that affect the rise and fall(ROC)of the New York Stock Exchange Composite Index.It was found that the proportion of stock price rise and fall(MOM),the return on S&P 500 index futures(SP),and the Russell 2000 index(RUT)have a significant impact on the rise and fall(ROC)of the New York Stock Exchange Composite Index.This demonstrates the effectiveness and practicality of the method used in this article.