In
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
can be written as,
:
where,
*
is the deterministic component (trend, seasonal component, etc.)
*
is the stochastic component.
*
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
98��154
Time series statistical tests