Bootstrap em modelos auto-regressivos aditivos generalizados

Abstract

The class of Generalized Additive Models (GAM), considered an extension of the Generalized Linear Models (GLM), is attracting the attention of researchers mainly due to the flexibility of these procedures. In spite of being built under the hypothesis of independency of the data, the GAM is widely applied to time series data, as an alternative to model variables such as trend and seasonality. Recently, more generalmodels, which consider the correlation structure among the data, like the GLARMA models (autoregressive moving average generalized linear models), are being used. This work extends the GLARMA models to a class of autoregressive generalized additive models of count series whose conditional distribution, given the past observations andthe independent variables, follows a Poisson distribution. Besides presenting the definition of the model, as well as the fitting procedures,this work employs, in a empirical study, the bootstrap procedure in three different ways (bootstrap in the observations, conditional bootstrap and the bootstrap in the residuals) in the interval inference of the parameters, comparing two bootstrap methods of building confidence intervals percentile bootstrap and bootstrap with bias correction. The results show that, in general, the procedures and the bootstrap confidence intervals present a satisfactory performance when used in the GAM models with the GLARMA structure, modeling count data with an autoregressive structure of order 1, and presenting estimates close to the true values of the parameters.