In this work, we present a modification of the hypothesis testing procedure for the existence of long memory in the stationary and invertible ARFIMA(p,d,q) process proposed by Castaño, Gómez and Gallón (2008). This modification allows assessing the existence of a fractional root in a...

This paper studies the properties of the sieve bootstrap for a class of linear processes which exhibit strong dependence. The sieve bootstrap scheme is based on residual resampling from autoregressive approximations the order of which increases slowly with the sample size. The first-order...

This paper investigates the empirical properties of autoregressive approximations to two classes of process for which the usual regularity conditions do not apply; namely the non-invertible and fractionally integrated processes considered in Poskitt (2006). In that paper the theoretical...

In this paper we will investigate the consequences of applying the sieve bootstrap under regularity conditions that are sufficiently general to encompass both fractionally integrated and non-invertible processes. The sieve bootstrap is obtained by approximating the data generating process by an...

Autoregressive models are commonly employed to analyze empirical time series. In practice, however, any autoregressive model will only be an approximation to reality and in order to achieve a reasonable approximation and allow for full generality the order of the autoregression, h say, must be...