Plenary lecture 3: computational methods in real life problem
Alina Bărbulescu · WSEAS international conference on Applied Computer and Applied Computational Science · 2012
The time series analysis is an ample domain of study, implying multiple approaches, in time and in frequency domain. The difficulties that appear in the modeling of the non - stationary time series are, essentially: the noise presence, the elaboration of the techniques of noise estimation and removal, the perturbations detection and measurement, the long dependence in the data series and the errors propagation. There is also the question on the accuracy of the entrance data. Generally, the models from the nature sciences have a deterministic a stochastic component. The pure stochastic models are used if the causality relations of the phenomena are not known. The pure deterministic ones are developed especially in meteorology and try to reproduce the dynamic of the rainfall field, based on Navier-Stokes equations, blunted, approximated and then numerical integrated (in the hypothesis of scale homogeneity). In spite of simplifying, the resulted equations remain complex, the calculation is difficult and the scales are independently studied one to others. So, the algorithm and the calculus methodology must be improved. There is the tendency to work in restrictive hypotheses on the data (stationarity, homoscedasticity, independence etc.) or one tries to bring them in standard form, by different transformations. But, in majority, the in nature sciences, the series are not stationary and heteroscedastic, needing decomposition procedures, to be modeled. In plus, they follow varied statistical laws and the data are not independent, presenting usually a long or short dependence in time. In our article we shall discuss this problems and their computational solution in modeling the time series, from classical ones (decomposition methods, deterministic models and stochastic models), to modern ones (GEP, AdaGEP and nonparametric), with concrete case study from meteorological time series.