Time series factorial models with uncertainty measures: applications to ARMA processes and financial data

In this paper, we propose a non-parametric structural approach in order to define new pertinent criterion in the selection process of time series. This approach combines a technical analysis of oscillators derived from Wilder (1978) and the Shannon (1948) theory of information, with factorial techniques of visualization.
In identifying classes of times series, using reference graphic models and pertinent criteria to better select appropriate models, this structural approach must be a first process to forecast models on significant entropies.
First, we apply this approach on simulated ARMA processes, to show significant groupings and oppositions explained by entropies, and to return some well known properties of autocorrelations functions. In the second one, we use the methodology to derive groups of funds based on their ratings. We observe that the Luxembourg funds are characterized by reductions of incertitude measured on Europerformance ratings against the French funds which are characterized by reductions of incertitude on Morningstar ratings, according their performance with incertitude reductions measured on daily returns.