Time Series Unit Root Test Comparison

The unit root test is a test method for testing the stability of time series, and it has a wide range of applications in the theoretical an experimental research in the field of economic and financial. And it is the basis of cointegration analysis and modeling.There are various forms of non-stationary time series, such as non-stationary time series that contain deterministic trend items, seasonal items, or heteroscedasticity respectively. We can use least squares fitting method, recognition method and differential method for smooth processing, thereby establishing various linear models which based on stationary series.Characterize the steady state of the dynamic system the ARMA series autoregressive polynomial root distribution characteristics of the Z plane containing the unit root time series presents the cycle changes, generally exhibit significant memory and persistent volatility. Cycle phenomena such as the continued volatility in the economy, the number of phenomena of concern to people, so effective testing methods for exploring and comparing time series unit root is necessary, the unit root test theories and methods makes sense.Since Dickey put forward theory of unit root test in1976, through continuous improvement, there are a variety of unit root test, such as Dickey Fuller test, the argumented Dickey Fuller test, trendingtest, structural mutations unit test have emerged.This paper summarized unit root test theory and some other methods obtained before by using classical unit root test method, higher efficient unit root test method and other types of unit root test methods.In the introduction part, it introduced the meaning, backround, and research status and the development trend of unit root test both at home and abroad, as well as four typical non-stationary random process. The Dickey Fuller test, the augmented Dickey Fuller test and Philip Perron test constitute for classic unit root test. Dickey Fuller test is the most foudamental unit root test, and other methods are its expand forms. This article derived the limit distribution and statistics focus of Dickey Fuller test under five kinds of situations. Augmented Dickey Fuller test and Philip Perron test only give statistics. Also the scope of application of the classical unit root test and different points were given.Classical unit root test has the poor seized effect in the case of small sample. In order to improve the testing effect, it advanced some more effective testing methods. They are Trending Unit Test, the RMA inspectionand WS test, etc. And the test statistic and the basic theory were given at the same time.To other unit root tests, it summarized six methods such as the panel data unit root test, variance ratio test, seasonal unit root test, etc.