The paper concerns the determination of statistical climate properties, a problem especially important for climate prediction validation. After a brief review of the times series analyses applied on secular series of observations, an appropriate method is described for characterizing these properties which finally reduces itself to the search for existing change-points. The examples of the Jones North Hemispheric land temperature averages (1856–1995) and of the Prague Klementinum ones (1771–1993) are given and results discussed. Relating the observed chaotic character of the climatological series to the non-linearity of the equations ruling the weather and thus climate evolution, and presenting the example of a solution of the Lorenz non-linear equations showing that non-linearity may be responsible for the instability of the generated process, it seems justified to conclude that there are severe limits to climate predictability at all scales. © 1997 John Wiley & Sons, Ltd.