# Phillips–Perron test

In statistics, the Phillips–Perron test (named after Peter C. B. Phillips and Pierre Perron) is a unit root test.[1] 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 of the null hypothesis ${\displaystyle \rho =1}$ in ${\displaystyle \Delta y_{t}=(\rho -1)y_{t-1}+u_{t}\,}$, where ${\displaystyle \Delta }$ is the first difference operator. Like the augmented Dickey–Fuller test, the Phillips–Perron test addresses the issue that the process generating data for ${\displaystyle y_{t}}$ might have a higher order of autocorrelation than is admitted in the test equation—making ${\displaystyle y_{t-1}}$ endogenous and thus invalidating the Dickey–Fuller t-test. Whilst the augmented Dickey–Fuller test addresses this issue by introducing lags of ${\displaystyle \Delta y_{t}}$ 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 and heteroscedasticity in the disturbance process of the test equation.