The Problem Of Gradual Changes In Panel Data Model

Compared with single time series,panel data has many advantages in testing and estimating the change points.While it may be difficult to identify a change point with a single series,it should be,intuitively,much easier to locate the common change point using a number of series together.The problem of change point in panel data can be divided into two categories according to its changing trend: abrupt change point and gradual change point.We focus on the latter,and study the problem of gradual change in panel data.In this paper,the research on the gradual changes of panel data is divided into two parts: test and estimation.The content of this paper as follows:Firstly,the test problem of the gradual changes in means of panel data is studied.The ratio test statistics are constructed.The limit properties are obtained under the null and alternative hypothesis,and the results of Monte Carlo show the estimations on panel data are better than that on single time series when the number of observations on each time series is the same.Secondly,the estimation problem of the gradual changes in means of panel data is studied.The least squares estimators of the changes are established,and the consistency and the convergence rate of the estimators are derived.The results from both numerical simulation and real data analysis support the argument.Finally,the estimation problem of the gradual changes in variances of panel data is studied.The problem of gradual changes in variances is transformed into the gradual change problem in means.The least squares estimators of the changes in means of the transformed model is established,both the consistency and the convergence rate of the estimators are derived.The results of Monte Carlo are shown to support the argument.