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Fractionally Integrated VAR Models with a Fractional Lag Operator and Deterministic Trends: Finite Sample Identification and Two-step Estimation

Author

Listed:
  • Tschernig, Rolf
  • Weber, Enzo
  • Weigand, Roland

Abstract

Fractionally integrated vector autoregressive models allow to capture persistence in time series data in a very flexible way. Additional flexibility for the short memory properties of the model can be attained by using the fractional lag perator of Johansen (2008) in the vector autoregressive polynomial. However, it also makes maximum likelihood estimation more diffcult. In this paper we first identify parameter settings for univariate and bivariate models that suffer from poor identification in finite samples and may therefore lead to estimation problems. Second, we propose to investigate the extent of poor identification by using expected log-likelihoods and variations thereof which are faster to simulate than multivariate finite sample distributions of parameter estimates. Third, we provide a line of reasoning that explains the finding from several univariate and bivariate simulation examples that the two-step estimator suggested by Tschernig, Weber, and Weigand (2010) can be more robust with respect to estimating the deterministic components than the maximum likelihood estimator.

Suggested Citation

  • Tschernig, Rolf & Weber, Enzo & Weigand, Roland, 2013. "Fractionally Integrated VAR Models with a Fractional Lag Operator and Deterministic Trends: Finite Sample Identification and Two-step Estimation," University of Regensburg Working Papers in Business, Economics and Management Information Systems 471, University of Regensburg, Department of Economics.
    • Handle: RePEc:bay:rdwiwi:27269
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    References listed on IDEAS

    as
    1. Shimotsu, Katsumi, 2010. "Exact Local Whittle Estimation Of Fractional Integration With Unknown Mean And Time Trend," Econometric Theory, Cambridge University Press, vol. 26(2), pages 501-540, April.
    2. Johansen, Søren & Nielsen, Morten Ørregaard, 2010. "Likelihood inference for a nonstationary fractional autoregressive model," Journal of Econometrics, Elsevier, vol. 158(1), pages 51-66, September.
    3. Morten Orregaard Nielsen, 2004. "Efficient inference in multivariate fractionally integrated time series models," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 63-97, June.
    4. Johansen, SØren, 2008. "A Representation Theory For A Class Of Vector Autoregressive Models For Fractional Processes," Econometric Theory, Cambridge University Press, vol. 24(3), pages 651-676, June.
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    Cited by:

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    2. Federico Carlini & Paolo Santucci de Magistris, 2019. "On the Identification of Fractionally Cointegrated VAR Models With the Condition," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(1), pages 134-146, January.
    3. Tobias Hartl, 2021. "Monitoring the pandemic: A fractional filter for the COVID-19 contact rate," Papers 2102.10067, arXiv.org.
    4. Hartl, Tobias, 2021. "Monitoring the pandemic: A fractional filter for the COVID-19 contact rate," VfS Annual Conference 2021 (Virtual Conference): Climate Economics 242380, Verein für Socialpolitik / German Economic Association.

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    More about this item

    Keywords

    fractional integration; long memory; maximum likelihood estimation; fractional lag operator;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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