A aproximação global no problema inverso das séries temporais

Abstract

The method of global approach is the axis of a theory for predicting and dynamic characteristics of time series. Theorems in the branch of differential topology are the mathematical basis for this method. The minimization of a cost function by the least squares method determines the predictor. In this process, the Shapiro-Wilk test evaluates if the normal distribution is a good approach to residuals in global mapping. The computational routines presented in this work implement the theory and perform the calculation of a quantity that increases the accuracy of the global forecast. The theory and computational procedures are compatible with different prediction times. The method establishes a confidence level in prediction, permits accurate forecasts and requires low runtimes. Criteria to control the quality of the global mappings are present in the computational routines. A kind of diagram developed in this paper uses results of the global approach to characterise the dynamics of a system from the time series. A computational program determines a new quantifier of chaos. Both the test of theory and the evaluation of the computational routines employ data that have their origin in simulated data or complex phenomena of real-world.