Small-sample likelihood-based inference in the ARFIMA model

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