This document discusses testing for non-stationarity and unit roots in time series data. It introduces the Augmented Dickey-Fuller (ADF) test and Phillips-Perron test for determining if a time series is integrated of order zero (I(0)), one (I(1)), or two (I(2)). The ADF test regressions the change in a variable on its lag and lags of the change to test for a unit root. If the null of a unit root is not rejected, further tests are needed to determine higher orders of integration. While ADF and Phillips-Perron tests are commonly used, their power is low if the process is near but not at the non-station