Inference and forecasting for ARFIMA models, with an application to US and
UK inflation

May 2003

by Jurgen A. Doornik and  Marius Ooms

Abstract: Practical aspects of likelihood-based inference and forecasting
of series with long memory are considered, based on the arfima(p; d; q) model
with deterministic regressors. Sampling characteristics of approximate and ex-
act first-order asymptotic methods are compared. The analysis is extended using
modified profile likelihood analysis, which is a higher-order asymptotic method
suggested by Cox and Reid (1987). The relevance of the differences between
the methods is investigated for models and forecasts of monthly core consumer
price inflation in the US and quarterly overall consumer price inflation in the
UK.
Keywords: ARFIMA; Bootstrap; Forecasting; GARCH; Maximum Likelihood;
Modified Profile Likelihood.

JEL Classification: C22, C53, C63.


Nuffield College, University of Oxford, Oxford OX1 1NF, UK. Email: jur-
gen.doornik@nuffield.ox.ac.uk.

Department of Economics, Free University of Amsterdam, 1081 HV Amsterdam, The
Netherlands. Email: m-
ooms@feweb.vu.nl.