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 I(1). It builds on the Dickey–Fuller test of the null hypothesis $\delta =0$ in $\nabla y_{t}=\delta y_{t-1}+u_{t}\,$, 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 $y_{t}$ might have a higher order of autocorrelation than is admitted in the test equation - making $y_{t-1}$ endogenous and thus invalidating the Dickey–Fuller t-test. Whilst the augmented Dickey–Fuller test addresses this issue by introducing lags of $\nabla y_{t}$ 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.

Reference

• Phillips, P.C.B and P. Perron (1988), "Testing for a Unit Root in Time Series Regression", Biometrika, 75, 335–346