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statistics Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...
, a unit root test tests whether a time series variable is non-stationary and possesses a unit root. The null hypothesis is generally defined as the presence of a unit root and the alternative hypothesis is either stationarity, trend stationarity or explosive root depending on the test used.


General approach

In general, the approach to unit root testing implicitly assumes that the time series to be tested _t^T can be written as, :y_t = D_t + z_t + \varepsilon_t where, * D_t is the deterministic component (trend, seasonal component, etc.) * z_t is the stochastic component. * \varepsilon_t is the stationary error process. The task of the test is to determine whether the stochastic component contains a unit root or is stationary.


Main tests

Other popular tests include: *
augmented Dickey–Fuller test In statistics, an augmented Dickey–Fuller test (ADF) tests the null hypothesis that a unit root is present in a time series sample. The alternative hypothesis is different depending on which version of the test is used, but is usually stationari ...
*: this is valid in large samples. *
Phillips–Perron test In statistics, the Phillips–Perron test (named after Peter C. B. Phillips and Pierre Perron) is a unit root test. That is, it is used in time series analysis to test the null hypothesis that a time series is integrated of order 1. It builds ...
* KPSS test *: here the null hypothesis is trend stationarity rather than the presence of a unit root. * ADF-GLS test Unit root tests are closely linked to serial correlation tests. However, while all processes with a unit root will exhibit serial correlation, not all serially correlated time series will have a unit root. Popular serial correlation tests include: * Breusch–Godfrey test * Ljung–Box test * Durbin–Watson test


Notes


References


"2007 revision"
* *{{cite book , last=Maddala , first=G. S. , authorlink=G. S. Maddala , last2=Kim , first2=In-Moo , chapter=Issues in Unit Root Testing , title=Unit Roots, Cointegration, and Structural Change , url=https://archive.org/details/unitrootscointeg00madd , url-access=limited , location=Cambridge , publisher=Cambridge University Press , year=1998 , isbn=0-521-58782-4 , page
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��154 Time series statistical tests