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Fractional integration with Drift: Estimation in Small Samples

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Abstract

We examine the finite-sample behavior of estimators of the order of integration in a fractionally integrated time-series model. In particular, we compare exact time-domain likelihood estimation to frequency-domain approximate likelihood estimation. We show that over-differencing is of critical importance for time-domain maximum-likelihood estimation in finite samples. Over-differencing moves the differencing parameter (in the over-differenced model) away from the boundary of the parameter space, while at the same time obviating the need to estimate the drift parameter. The two estimators that we compare are asymptotically equivalent. In small samples, however, the time-domain estimator has smaller mean squared error than the frequency-domain estimator. Although the frequency-domain estimator has larger bias than the time-domain estimator for some regions of the parameter bias, it can also have smaller bias. We use a simulation procedure which exploits the approximate linearity of the bias function to reduce the bias in the time-domain estimator.
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  • Tony Smith & Fallaw Sowell & Stanley Zin, "undated". "Fractional integration with Drift: Estimation in Small Samples," GSIA Working Papers 22, Carnegie Mellon University, Tepper School of Business.
  • Handle: RePEc:cmu:gsiawp:22
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    Cited by:

    1. MacKinnon, James G. & Smith Jr., Anthony A., 1998. "Approximate bias correction in econometrics," Journal of Econometrics, Elsevier, vol. 85(2), pages 205-230, August.
    2. Perez, Ana & Ruiz, Esther, 2001. "Finite sample properties of a QML estimator of stochastic volatility models with long memory," Economics Letters, Elsevier, vol. 70(2), pages 157-164, February.
    3. Stelios Arvanitis & Antonis Demos, 2015. "A class of indirect inference estimators: higher‐order asymptotics and approximate bias correction," Econometrics Journal, Royal Economic Society, vol. 18(2), pages 200-241, June.
    4. Derek Bond & Michael J. Harrison & Edward J. O'Brien, 2005. "Testing for Long Memory and Nonlinear Time Series: A Demand for Money Study," Trinity Economics Papers tep20021, Trinity College Dublin, Department of Economics.
    5. Carlos Pestana Barros & Luis Gil-Alana, 2006. "Eta: A Persistent Phenomenon," Defence and Peace Economics, Taylor & Francis Journals, vol. 17(2), pages 95-116.
    6. Doornik, Jurgen A. & Ooms, Marius, 2003. "Computational aspects of maximum likelihood estimation of autoregressive fractionally integrated moving average models," Computational Statistics & Data Analysis, Elsevier, vol. 42(3), pages 333-348, March.
    7. Ana Pérez & Esther Ruiz, 2002. "Modelos de memoria larga para series económicas y financieras," Investigaciones Economicas, Fundación SEPI, vol. 26(3), pages 395-445, September.
    8. Doornik Jurgen A & Ooms Marius, 2004. "Inference and Forecasting for ARFIMA Models With an Application to US and UK Inflation," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(2), pages 1-25, May.
    9. Doornik, Jurgen A. & Ooms, Marius, 2003. "Computational aspects of maximum likelihood estimation of autoregressive fractionally integrated moving average models," Computational Statistics & Data Analysis, Elsevier, vol. 42(3), pages 333-348, March.

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