In
statistics, the Phillips–Perron test (named after
Peter C. B. Phillips and
Pierre Perron) is 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 ...
test. That is, it is used in
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 ...
analysis to test the
null hypothesis
In scientific research, the null hypothesis (often denoted ''H''0) is the claim that no difference or relationship exists between two sets of data or variables being analyzed. The null hypothesis is that any experimentally observed difference is d ...
that a time series is
integrated of order 1. It builds on the
Dickey–Fuller test of the null hypothesis
in
, where
is the
first difference operator. Like the
augmented Dickey–Fuller test, 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
A ''t''-test is any statistical hypothesis test in which the test statistic follows a Student's ''t''-distribution under the null hypothesis. It is most commonly applied when the test statistic would follow a normal distribution if the value of ...
. 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
Nonparametric statistics is the branch of statistics that is not based solely on parametrized families of probability distributions (common examples of parameters are the mean and variance). Nonparametric statistics is based on either being distri ...
correction to the t-test statistic. The test is robust with respect to unspecified
autocorrelation and
heteroscedasticity 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