Small-sample likelihood-based inference in the Arfima model

Offer Lieberman*, Judith Rousseau, David M. Zucker

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


The autoregressive fractionally integrated moving average (ARFIMA) model has become a popular approach for analyzing time series that exhibit long-range dependence. For the Gaussian case, there have been substantial advances in the area of likelihood-based inference, including development of the asymptotic properties of the maximum likelihood estimates and formulation of procedures for their computation. Small-sample inference, however, has not to date been studied. Here we investigate the small-sample behavior of the conventional and Bartlett-corrected likelihood ratio tests (LRT) for the fractional difference parameter. We derive an expression for the Bartlett correction factor. We investigate the asymptotic order of approximation of the Bartlett-corrected test. In addition, we present a small simulation study of the conventional and Bartlett-corrected LRT's. We find that for simple ARFIMA models both tests perform fairly well with a sample size of 40 but the Bartlett-corrected test generally provides an improvement over the conventional test with a sample size of 20.

Original languageAmerican English
Pages (from-to)231-248
Number of pages18
JournalEconometric Theory
Issue number2
StatePublished - 2000


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