Stationarity tests
The three best-known tests for stationarity (or rather, unit roots) in time series econometrics are:
- Dickey-Fuller including Augmented Dickey-Fuller
- Phillips-Perron
- KPSS
There are also Bayesian tests of unit roots, as implemented in this conference presentation. If you have access to JSTOR or another way of getting at old journals, this article might be of interest.
As far as I'm aware, nobody has created a pre-digested package for unit root testing in Mathematica. The notebook I wrote - about a decade ago - only includes the KPSS test, and I can give no warranties about whether I did it right. It was written for version 3 and would need considerable updating to work with version 8, as it has dependencies on several packages that have been made obsolete when the functionality was rolled into the main kernel.
The Dickey-Fuller and the Phillips-Perron tests are now available using UnitRootTest, introduced in Mathematica 9.