The Unit Root Test With Structural Break And Its Application In The Time Series

Unit root test is the basis of time series analysis, Before analysis or modeling of a time series, it need to have stationary test. Because the stationary and non-stationary variables have different statistical properties and economic meanings, the methods of mathematical statistics and econometrics are different. Especially for non-stationary time series, central limit theorem is not applicable. Unit root test is a kind of commonly tools to have stationary test. Unit root process and trend stationary process is the most common type of non-stationary process. In practice, to distinguish the non-stationary variables is whether a trend stationary process or a unit root process is of great significance. Regardless of the structural break composition of unit root test will often get the wrong conclusion that mistaking a trend stationary process for unit root process, so the unit root test with structural break is an important research significance.Introducing the research background and significance of this article, summarizing the history research work of unit root test with structural break. The unit root test with structural break is divided into two main classes, unit root test with exogenous structural break and unit root test with endogenous structural break. Then introducing the unit root process and trend stationary process, and giving several different unit root test model with structural break. This paper introduces the hidden Markov model into the unit root test with structural break. Firstly based on hidden Markov model to detect the structural break point to build dummy variable structure, determine the regression model, finally have unit root test on the sequence by eliminating tendency. And using this method to test the unit root with structural break on the consumer price index in China, getting the conclusion that Chinese consumer price index is a structural break trend stationary process, and the model on Chinese consumer price index has a better fitting effect.Usually we assume that the trend function is linear, so this paper also use a unit root test with nonlinear trend, eliminating tendency by singular value decomposition and recursive average adjustment unit root test (SVD-RMA), to make an empirical analysis of the total retail sales of social consumer goods in China, the empirical analysis show that the total retail sales of social consumer goods is a trend stationary process. And in order to validate the conclusion, also using the unit root test with exogenous structural break to test the retail sales of social consumer goods in China, Results show that the retail sales of social consumer goods in China is a trend stationary process containing two break points. The change may be caused by the shift of fiscal policy belonging to the macroeconomic regulation and control.