Time Series Factorial Models with Uncertainty Measures: Applications to ARMA Processes and Financial Data

Abstract

To facilitate the task of identifying time series classes, we propose a nonparametric approach to defining new pertinent criteria. This approach combines a technical analysis of series of states and theory of information with factorial techniques of visualization. First, we apply this approach to the usual benchmarks in time series analysis, i.e., simulated ARMA processes. We show significant groupings and oppositions explained by entropies returning some well-known properties of autocorrelation functions. Having thus justified the methodology, we apply it to practical financial data. Second, we use the approach with entropies or uncertainty measures to analyze risk information in fund ratings and returns. The financial data analysis is applied to a set of 1500 European equity funds with both Morningstar and Europerformance ratings, for the period from 2005–2007. Our methodology derives groups of funds with high to low uncertainty measured on Morningstar ratings against low to high uncertainty on Europerformance, and conversely. We conclude that the two agencies provide different classifications of funds, and that, in a more general case, the higher predictive power is offered by the Morningstar ratings.