Intervalos de previsão em modelos ARFIMA utilizando a metodologia Bootstrap

Abstract

The traditional methods of building prediction intervals for time series assume that the model parameters are known and the errors are Gaussian. When such assumptions are not true, the prediction intervals possess a coverage different from the nominal one. This work proposes the use of the bootstrap methodology to build prediction intervals with coverage closer to the nominal. Two bootstrap intervals are used, the PRR interval and the EPB interval. The PRR interval is an adaptation for the ARFIMA model of the homonimous interval proposed by Pascual et al. (2004) for the ARIMA model. The EPB interval proposed in this work is similar to intervals proposed for time series models, such as the one of Masarotto (1990) for autoregressive models. Bootstrap bias corrections, including the bias of the residuals standard deviation, are tested as possible sources of improvement for the intervals. The methods used in this work were also tested for ARMA series. The work concludes that the PRR and EPB intervals improve significantly the quality of the prediction intervals in comparison with asymptotic one, and the bootstrap bias corrections of the residuals standard deviation may also be useful on that goal.