Introduction

We have heard many times during this conference that variability is a powerful tool to investigate the nature of AGN. The goal of this talk is to demonstrate that the clues derived from variability studies may be partial, disappointing and even misleading, if some characteristics of variability are overlooked and the proper statistical tools are not adopted. To convince you that such a caveat, although obvious, is important and productive, we should like to focus on a few issues, particularly important from our point of view.

The stochastic nature of the light curves

First of all, let's draw your attention to the fact that light curves of quasars have generally random behaviour, i.e., that the knowledge of the value of a time series at a given instant does not allow (in a broad sense) one to forecast the future evolution of the light curve. What does it mean from a physical point of view? It means that quasars are dynamical systems of high dimensionality, systems whose temporal evolution is described by an extremely large set of differential equations (or by partial differential equations). In other words, quasars are dynamical systems whose evolution is determined by a large number of external factors. To understand this point let us consider an example close to common sense: a pendulum. As is well known, the temporal evolution of such a system is described by a second order ordinary differential equation.