Bootstrap estacionario em modelos ARFIMA (p,d,q)

Abstract

This study aims to use the stationary bootstrap to make inference about the memory parameter, d, in ARFIMA models and verify its efficiency in the region of stationarity. The method consists of using the stationary bootstrap to resample a data set using the geometric and uniform distributions. The length of each block that composes the bootstrap series is obtained through the geometric distribution and the starting point of each block is generated by a uniform distribution. In this work, the estimation of the memory parameter of ARFIMA models is performed through semiparametric and maximum likelihood methods. Bootstrap percentile and bias corrected confidence intervals are also constructed and their performances are analyzed by the coverage rate of the intervals. Monte Carlo simulation studies showed that lower values of the parameter used in the geometric distribution generate estimates of d closer to the actual value, especially when using the semiparametric procedure. Moreover, the results also show that the percentile confidence intervals have coverage rates closer to the fixed nominal value of 95% than the interval BC.