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Alternative Forms of Fractional Brownian Motion - (Now published in Journal of Statistical Planning and Inference, 80 (1999), pp.111-122.)

Author

Listed:
  • D Marinucci
  • Peter M Robinson

Abstract

It is pointed out that two contradictory definitions of fractional Brownian motion are well established, one prevailing in the probabilistic literature, the other in the econometric literature. Each is associated with a different definition of nonstationary fractional time series. These various definitions have occasionally led to some confusion. The paper discusses the definitions and attempts a clarification.

Suggested Citation

  • D Marinucci & Peter M Robinson, 1998. "Alternative Forms of Fractional Brownian Motion - (Now published in Journal of Statistical Planning and Inference, 80 (1999), pp.111-122.)," STICERD - Econometrics Paper Series 354, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    • Handle: RePEc:cep:stiecm:354
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    File URL: https://sticerd.lse.ac.uk/dps/em/em354.pdf
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    Citations

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    Cited by:

    1. Guglielmo Caporale & Luis Gil-Alana, 2014. "Fractional integration and cointegration in US financial time series data," Empirical Economics, Springer, vol. 47(4), pages 1389-1410, December.
    2. Peter M Robinson, 2004. "The Distance between Rival Nonstationary Fractional Processes," STICERD - Econometrics Paper Series 468, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    3. Nielsen, Morten Ørregaard & Frederiksen, Per, 2008. "Finite sample accuracy and choice of sampling frequency in integrated volatility estimation," Journal of Empirical Finance, Elsevier, vol. 15(2), pages 265-286, March.
    4. Morten Ørregaard Nielsen & Per Houmann Frederiksen, 2005. "Finite Sample Comparison of Parametric, Semiparametric, and Wavelet Estimators of Fractional Integration," Econometric Reviews, Taylor & Francis Journals, vol. 24(4), pages 405-443.
    5. Javier Hualde & Peter M Robinson, 2003. "Cointegration in Fractional Systems with Unkown Integration Orders," STICERD - Econometrics Paper Series 449, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    6. Nielsen, Morten Orregaard & Shimotsu, Katsumi, 2007. "Determining the cointegrating rank in nonstationary fractional systems by the exact local Whittle approach," Journal of Econometrics, Elsevier, vol. 141(2), pages 574-596, December.
    7. Seong Yeon Chang & Pierre Perron, 2016. "Inference on a Structural Break in Trend with Fractionally Integrated Errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(4), pages 555-574, July.
    8. Dietmar Bauer & Alex Maynard, 2010. "Persistence-robust Granger causality testing," Working Papers 1011, University of Guelph, Department of Economics and Finance.
    9. Hualde, Javier, 2006. "Unbalanced Cointegration," Econometric Theory, Cambridge University Press, vol. 22(5), pages 765-814, October.
    10. Martins, Luis F. & Rodrigues, Paulo M.M., 2014. "Testing for persistence change in fractionally integrated models: An application to world inflation rates," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 502-522.
    11. Hualde Javier & Iacone Fabrizio, 2012. "First Stage Estimation of Fractional Cointegration," Journal of Time Series Econometrics, De Gruyter, vol. 4(1), pages 1-32, May.
    12. Gil-Alana, Luis A. & Fischer, Christian, 2007. "International traveling and trade: further evidence for the case of Spanish wine based on fractional VAR specifications," 105th Seminar, March 8-10, 2007, Bologna, Italy 7859, European Association of Agricultural Economists.

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