In
statistics, a unit root test tests whether a
time series
In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Ex ...
variable is non-stationary and possesses a
unit root
In probability theory and statistics, a unit root is a feature of some stochastic processes (such as random walks) that can cause problems in statistical inference involving time series models. A linear stochastic process has a unit root if 1 is ...
. 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
*: 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 In econometrics, Kwiatkowski–Phillips–Schmidt–Shin (KPSS) tests are used for testing a null hypothesis that an observable time series is stationary around a deterministic trend (i.e. trend-stationary) against the alternative of a unit root.
...
*: here the null hypothesis is
trend stationarity rather than the presence of a
unit root
In probability theory and statistics, a unit root is a feature of some stochastic processes (such as random walks) that can cause problems in statistical inference involving time series models. A linear stochastic process has a unit root if 1 is ...
.
*
ADF-GLS test
In statistics and econometrics, the ADF-GLS test (or DF-GLS test) is a test for a unit root in an economic time series sample. It was developed by Elliott, Rothenberg and Stock (ERS) in 1992 as a modification of the augmented Dickey–Fuller test
...
Unit root tests are closely linked to
serial correlation
Autocorrelation, sometimes known as serial correlation in the discrete time case, is the correlation of a signal with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations of a random variable a ...
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
In statistics, the Breusch–Godfrey test is used to assess the validity of some of the modelling assumptions inherent in applying regression-like models to observed data series. In particular, it tests for the presence of serial correlation th ...
*
Ljung–Box test
The Ljung–Box test (named for Greta M. Ljung and George E. P. Box) is a type of statistical test of whether any of a group of autocorrelations of a time series are different from zero. Instead of testing randomness at each distinct lag, it tes ...
*
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