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Small-Sample Likelihood-Based Inference In The Arfima Model

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  • Lieberman, Offer
  • Rousseau, Judith
  • Zucker, David M.

Abstract

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.

Suggested Citation

  • Lieberman, Offer & Rousseau, Judith & Zucker, David M., 2000. "Small-Sample Likelihood-Based Inference In The Arfima Model," Econometric Theory, Cambridge University Press, vol. 16(2), pages 231-248, April.
    • Handle: RePEc:cup:etheor:v:16:y:2000:i:02:p:231-248_16
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    Cited by:

    1. La Vecchia, Davide & Ronchetti, Elvezio, 2019. "Saddlepoint approximations for short and long memory time series: A frequency domain approach," Journal of Econometrics, Elsevier, vol. 213(2), pages 578-592.
    2. Marcelo Resende, 2012. "Long Memory in Mergers and Acquisitions: Sectoral Evidence for an Emerging Economy," Economics Bulletin, AccessEcon, vol. 32(4), pages 2876-2883.
    3. Beran, Jan & Ghosh, Sucharita & Schell, Dieter, 2009. "On least squares estimation for long-memory lattice processes," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2178-2194, November.

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