How does @RISK try to achieve stationarity in fitting data to time series? Does the "Auto Detect" button use the Dickey-Fuller test or KPSS?

The first thing to say is that, without knowing the source of the data, it's impossible to do auto detect perfectly; by necessity, it's a heuristic. When you choose Auto Detect, you need to look at the result and correct it as necessary, based on your knowledge of the source of the data,

The KPSS test isn't appropriate for @RISK, since we don't really support trend-stationary time-series. Currently we only detrend using differences, although that may change in future versions of @RISK.

The Dickey-Fuller (DF) test—or usually augmented Dickey-Fuller—is more appropriate, but @RISK does not use that either. The Analysis of Time Series by Chris Chatfield (Chapman & Hall, 2003) p. 263 is quite negative about unit root testing. At best, it would be some additional information that could help distinguish between difference-stationarity and trend-stationarity, if we ever add the latter to @RISK. The DF tests have an additional drawback: they generally assume you have already removed other things that are making the data non-stationary. The obvious hard one is seasonality, especially when combined with a functional transform. But it's Catch-22, because every paper we found with routines for determining the periodicity of seasonality assumes you have already removed trends. Therefore, we had to take a different approach.

@RISK uses a technique adapted from electronic signal processing. There, one takes small "windows" or subsets of the data, calculates statistics of these subsets, and then does standard statistical tests to compare if these statistics are changing as a function of time. @RISK looks through all the possible transformations (functional, detrending, and deseasonalization) to find the combination that produces acceptable test statistics. We also use proprietary techniques to address some nasty details: such as how to avoid over-differencing, how to determine the seasonal period, and so forth.