Indirect estimation of ARFIMA and VARFIMA models

Indirect estimation methods are proposed for estimating ARFIMA, as well as more complex VARFIMA models. A general framework for conducting indirect estimation of fractional models is developed that covers simulation methods, choice of auxiliary model and estimation algorithm. Special attention is given to comparing the finite sampling properties of the indirect estimator with Sowellʹs (1992a) exact time domain maximum-likelihood estimator, the spectral maximum-likelihood estimator of Fox and Taqqu (1986) and the Geweke and Porter-Hudak (1983) spectral regression estimator. The indirect estimator can be computationally faster than the exact time domain maximum-likelihood estimator while generating similar small sample properties. The computational gains of the indirect estimator over maximum likelihood increase as the complexity of the data generating process increases.