Econometricians often talk about a time series being integrated with order k, I(k). k being the minimum number of differences required to obtain a stationary time series.
What methods or statistical tests can be used to determine, given a level of confidence, the order of integration of a time series?
There are a number of statistical tests (known as “unit root tests”) for dealing with this problem. The most popular is probably the “Augmented Dickey-Fuller” (ADF) test, although the Phillips-Perron (PP) test and the KPSS test are also widely used.
Both the ADF and PP tests are based on a null hypothesis of a unit root (i.e., an I(1) series). The KPSS test is based on a null hypothesis of stationarity (i.e., an I(0) series). Consequently, the KPSS test can give quite different results from the ADF or PP tests.