Modelos de séries temporais com coeficientes variando no tempo - Souza, Leandro Teixeira Lopes de (2009)
In this work they are presented extensions of Auto Regressive and Auto Regressive Conditional Heteroscedasticity models with coefficients varying in time. These coefficients have been used as models for non stationary real time series, specially for financial series. The objective of this work is to present the models and the techniques involved in estimating time-varying coefficients, moreover, it is made an introduction to financial modeling and some suggestions in order to facilitate implementation and use of models with time-varying coefficients. The simulation studies and the application on real data showed that the models have great potential to be exploited in the analysis of non-stationary series. The suggestions in confidence band and forecasting for the Auto regressive models with time-varying coefficients enable the use of models in financial data and other series that show a non-stationary characteristic. The modified algorithm for estimation of ARCH models varying in time was to increase the rate of convergence. The creation of a method for forecasting for ARCH models require a deeper study, although the algorithm has shown promising results in simulation study, giving some evidences that it can be applied in real situation. Finally, the contributions in the creation of functions for a free software that facilitate the use and the analysis of the models studied and the use of the proposed methods.