AN AND JOS

Abstract. We describe a theoretical formalism for the dimensional analysis of arbitrary stationary time series. We use this setting to study which properties are to be satised by a dimension concept in order to discern chaotic time series from white noise. In particular it follows that correlation dimensions can dis-criminate chaotic time series from white noise processes with L 1 {marginals, but not from arbitrary white noise. We also justify how the dimensional anal-ysis can be put in practice using standard delay-embedding methods. 1