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The effect of additive outliers on a fractional unit root test

Author

Listed:
  • Christian M. Hafner

    () (Université Catholique de Louvain)

  • Arie Preminger

    (Ariel University
    Emek Yezreel Academic College)

Abstract

Abstract It is well known that additive outliers that occur with a small probability have a bias effect on the asymptotic distribution of classical unit root statistics. This paper shows that such outliers do not affect the asymptotic distribution in the case where the error term is fractionally integrated of order d, where $$0

Suggested Citation

  • Christian M. Hafner & Arie Preminger, 2016. "The effect of additive outliers on a fractional unit root test," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(4), pages 401-420, October.
  • Handle: RePEc:spr:alstar:v:100:y:2016:i:4:d:10.1007_s10182-015-0265-5
    DOI: 10.1007/s10182-015-0265-5
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    References listed on IDEAS

    as
    1. Pierre Perron & Gabriel RodrÌguez, 2003. "Searching For Additive Outliers In Nonstationary Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(2), pages 193-220, March.
    2. Eduardo Rossi & Paolo Santucci de Magistris, 2014. "Estimation of Long Memory in Integrated Variance," Econometric Reviews, Taylor & Francis Journals, vol. 33(7), pages 785-814, October.
    3. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    4. Neil Shephard & Kevin Sheppard, 2010. "Realising the future: forecasting with high-frequency-based volatility (HEAVY) models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(2), pages 197-231.
    5. Shin, Dong Wan & Sarkar, Sahadeb & Lee, Jong Hyup, 1996. "Unit root tests for time series with outliers," Statistics & Probability Letters, Elsevier, vol. 30(3), pages 189-197, October.
    6. Jussi Tolvi, 2003. "Long memory and outliers in stock market returns," Applied Financial Economics, Taylor & Francis Journals, vol. 13(7), pages 495-502.
    7. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July.
    8. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    9. Franses, Philip Hans & Haldrup, Niels, 1994. "The Effects of Additive Outliers on Tests for Unit Roots and Cointegration," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 471-478, October.
    10. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    11. Chung, Ching-Fan & Baillie, Richard T, 1993. "Small Sample Bias in Conditional Sum-of-Squares Estimators of Fractionally Integrated ARMA Models," Empirical Economics, Springer, vol. 18(4), pages 791-806.
    12. Haldrup, Niels & Nielsen, Morten Orregaard, 2007. "Estimation of fractional integration in the presence of data noise," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 3100-3114, March.
    13. David F. Hendry & Carlos Santos, 2005. "Regression Models with Data-based Indicator Variables," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 67(5), pages 571-595, October.
    14. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    15. Hansen, Peter R. & Lunde, Asger, 2014. "Estimating The Persistence And The Autocorrelation Function Of A Time Series That Is Measured With Error," Econometric Theory, Cambridge University Press, vol. 30(01), pages 60-93, February.
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    17. repec:bla:jtsera:v:20:y:1999:i:5:p:565-577 is not listed on IDEAS
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    More about this item

    Keywords

    Fractional Brownian motion; Additive outliers; Long memory; Unit root;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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