Stability of ARCH models and unit root tests

In time series analysis, the stationarity takes an important place. Indeed, stationary processes are more tractable in prcatice and mathematical analysis. In the speciale case of autoregressive models, the stationarity is connected with the unit root problem. Some main published results, such as the famous Dickey-Fuller test, are presented in the first part of the document. Our aim is to study the behavior of this test in presence of contamination. The second part which is independent on the first,treats some aspects of ARCH models (autoregressive conditionally heteroscedastic) that are non linear processes. However, since unit root tests and ARCH models are connected, we preferred to present them in a same document.