Inferência sobre modelos de regressão linear com pontos de mudança e erros normais autoregressivos

Abstract

Linear regression analysis models are some of the most important techniques in Statistics. With it, it’s possible to identify relationships between variables that visual techniques, sometimes, do not show. However, to procede with linear regression analysis, too many assumptions must be satisfied. A very important one, error independence, cannot always be satified, which may return residuals with autpcorrelation after fitting the proposed model. There are many techniques to deal with this correlation, but it can be interesting to the researcher to model the dependence of the errors which can improve the model fitting. Sometimes, the researcher is interested in identifying structural breaks in the mean and/or variance of some process which is suspeted to be not working correctly. In this situation, change-point identification is extremely useful. The aim of this monograph is to present the situation in which all of these scenarios are present: linear regression models, auto-regressive process and change-point; also to present estimates to this model.