  The problem of prediction of a given time series is examined on the basis of
recent nonlinear dynamics theories. Particular attention is devoted to forecast
the amplitude and phase of one of the most common solar indicator activity, the
international monthly smoothed sunspot number. It is well known that the solar
cycle is very difficult to predict due to the intrinsic complexity of the
related time behaviour and to the lack of a succesful quantitative theoretical
model of the Sun magnetic cycle. Starting from a previous recent work, we
checked the reliability and accuracy of a forecasting model based on concepts
of nonlinear dynamical systems applied to experimental time series, such as
embedding phase space, Lyapunov spectrum, chaotic behaviour. The model is based
on a local hypothesis of the behaviour on the embedding space, utilizing an
optimal number k of neighbour vectors to predict the future evolution of the
current point with the set of characteristic parameters determined by several
previous parametric computations. The performances of this method suggest its
valuable insertion in the set of the so-called statistical-numerical prediction
techniques, like Fourier analyses, curve fitting, neural networks,
climatological, etc. The main task is to set up and to compare a promising
numerical nonlinear prediction technique, essentially based on an inverse
problem, with the most accurate predictive methods like the so-called
"precursor methods" which appear now reasonably accurate in predicting "long
term" Sun activity, with particular reference to the "solar" precursor methods
based on a solar dynamo theory.
