Two Tests For Change In Persistence

During the passed twenty years,the research of change points attracts the attention of the statisticians and econometricians,and becomes a hot topic,and also has important appli-cations in the economics,finances and medical fields.There are many existing theoretical results on the case of statistics to distinguish between stationary models and the models with a change-point in persistence,however many macroeconomic data are unit root processes,and the existing methods can't distinguish the processes with a change in persistence from the unit root processes.Therefore,the paper proposes two tests for change in persistence under the null hypothesis of unit root.The first test is based on Haar wavelet decomposition,and the second is based on residualsFirstly,a test for change in persistence based on Haar wavelet decomposition is pro-posed.By the unit-scale wavelet and scale coefficients,the test is proposed and then its asymptotic distribution under the null hypothesis is obtained,and the asymptotic properties are shown respectively under the alternative hypotheses of I(0)-I(1)and I(1)-I(0).In addition,numerical simulations demonstrate that this test behaves better with a more correct size and a more high power when the change in persistence is not obvious.The method is t effective by the application on the data of the inflation rate in the United StatesSecondly,a ratio test for the change in persistence based on residuals is proposed The ratio statistic's asymptotic property under the null hypothesis is obtained,and the consistency under the alternative hypothesis is shown.Monte Carlo simulations show that,compared with R statistic proposed by Leybourne et al.[22],the new test can reduce the probability of the both types of errors,and the effect is still significant under the stationary hypothesis.The effectiveness of the method is illustrated by applications.