Statistical Inference Of Structural Change Points In Linear Regression Model With LMSV Errors

The change point problem has been a compelling topic in statistics since the 1970 s,and early methods of change point analysis were developed for independent observations and then extended to more complex dependent processes and regression models.Regarding the problem of structural change points in linear regression models,a large number of studies have been made on the cases where the error terms range from independent and identical distributions to dependence and then to heteroscedasticity.This paper studies the testing,monitoring,and estimation of structural change points in a linear regression model with long memory stochastic volatility errors which can exhibit both long memory and heteroscedasticity.Firstly,based on the least squares fitting residuals,a self-normalized CUSUM test statistic is proposed to test the structural change point,the limiting distribution of the test statistic is proved under the null hypothesis,and the consistency of the statistic is proved under the alternative hypothesis.A Sieve Bootstrap method is used to approximate the critical values of the test statistic.Numerical simulations show that the Sieve Bootstrap method can control the empirical size well,and the proposed test method can effectively detect change point.Moreover,we illustrate the feasibility of our method by modeling a set of PM2.5 and SO2 concentration data in the air of Xining and test the structural change points.Secondly,we propose a monitoring statistic,which is based on the least squares fitting residuals,to monitor structural change points in the linear regression model and derive its asymptotic distribution under the null hypothesis.The consistency of monitoring statistic under the alternative hypothesis has also been proved,and we applied a Sieve Bootstrap method to approximate its critical values.Numerical simulations show the proposed monitoring procedure can control the empirical size well,and has a satisfy empirical power and average run length.Finally,we use a statistic based on the least squares fitting residuals to estimate the change points.The finite sample properties of the estimator were studied through numerical simulations.Some histograms of the change point estimation intuitively show that the estimator has a small average absolute deviation and standard error.