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 ...
, the Phillips–Perron test (named after
Peter C. B. Phillips
Peter Charles Bonest Phillips (born 23 March 1948) is an econometrician. Since 1979 he has been Professor of Economics and Statistics at Yale University. He also holds positions at the University of Auckland, Singapore Management University and t ...
and
Pierre Perron
Pierre Perron (born March 14, 1959) is a Canadian econometrician at Boston University. Perron is known for the Phillips–Perron test of a unit root
In probability theory and statistics, a unit root is a feature of some stochastic processes ( ...
) 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 on the
Dickey–Fuller test
In statistics, the Dickey–Fuller test tests the null hypothesis that a unit root is present in an autoregressive time series model. The alternative hypothesis is different depending on which version of the test is used, but is usually stationa ...
of the null hypothesis
in
, where
is the
first difference operator
Operator may refer to:
Mathematics
* A symbol indicating a mathematical operation
* Logical operator or logical connective in mathematical logic
* Operator (mathematics), mapping that acts on elements of a space to produce elements of another ...
. Like the
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 ...
, the Phillips–Perron test addresses the issue that the process generating data for
might have a higher order of autocorrelation than is admitted in the test equation—making
endogenous and thus invalidating the Dickey–Fuller
t-test. Whilst the augmented Dickey–Fuller test addresses this issue by introducing lags of
as regressors in the test equation, the Phillips–Perron test makes a
non-parametric correction to the t-test statistic. The test is robust with respect to unspecified
autocorrelation
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 ...
and
heteroscedasticity
In statistics, a sequence (or a vector) of random variables is homoscedastic () if all its random variables have the same finite variance. This is also known as homogeneity of variance. The complementary notion is called heteroscedasticity. The s ...
in the disturbance process of the test equation.
Davidson and MacKinnon (2004) report that the Phillips–Perron test performs worse in finite samples than the augmented Dickey–Fuller test.
References
{{DEFAULTSORT:Phillips-Perron test
Statistical tests