Advertisement

Long-Range Dependence and ARFIMA Models

  • Ali ErcanEmail author
  • M. Levent Kavvas
  • Rovshan K. Abbasov
Chapter
Part of the SpringerBriefs in Statistics book series (BRIEFSSTATIST)

Abstract

In this chapter, long-range dependence concept, Hurst phenomenon and ARFIMA models are introduced and the earlier work on these subjects are reviewed. Several methodologies are introduced for the estimation of long-range dependence index (Hurst number or fractional difference parameter).

Keywords

Long-range dependence Long memory ARFIMA models Hurst phenomenon 

References

  1. Barbosa SM, Fernandes MJ, Silva ME (2006) Long-range dependence in North Atlantic sea level. Phys A 371(2):725–731CrossRefGoogle Scholar
  2. Beran J (1994) Statistics for long-memory processes. Chapman and Hall, New YorkzbMATHGoogle Scholar
  3. Beran J, Terrin N (1996) Testing for a change of the long-memory parameter. Biometrika 83(3):627–638MathSciNetzbMATHCrossRefGoogle Scholar
  4. Bloomfield P (1992) Trends in global temperature. Clim Change 21(1):1–16CrossRefGoogle Scholar
  5. Box, G.E.P, and Jenkins, G.M. (1976). Time series analysis: forecasting and control. Holden-Day, San FransiscoGoogle Scholar
  6. Box GEP, Jenkins GM, Reinsel GC (2008) Time series analysis: forecasting and control. Wiley, HobokenzbMATHGoogle Scholar
  7. Brockwell PJ, Davis RA (1987) Time series: theory and methods. Springer, New YorkzbMATHGoogle Scholar
  8. Crato N, Ray BK (1996) Model selection and forecasting for long-range dependent processes. J Forecast 15:107–125CrossRefGoogle Scholar
  9. Dahlhaus R (1989). Efficient parameter estimation for self-similar processes. Ann Stat 17, 1749–1766Google Scholar
  10. Eltahir EAB (1996) El Nino and the natural variability in the flow of the Nile River. Water Resour Res 32(1):131–137CrossRefGoogle Scholar
  11. Fox R, Taqqu MS (1986) Large-sample properties of parameter estimates for strongly dependent stationary gaussian time series. The Ann Stat 14(2):517–532MathSciNetzbMATHCrossRefGoogle Scholar
  12. Geweke J, Porter-Hudak S (1983) The estimation and application of long memory time series models. J Time Ser Anal 4(4):221–238MathSciNetzbMATHCrossRefGoogle Scholar
  13. Granger CWJ, Joyeux R (1980) An introduction to long memory time series models and fractional differencing. J Time Ser Anal 1:15–29MathSciNetzbMATHCrossRefGoogle Scholar
  14. Haslett J, Rafterv AE (1989) Space-time modelling with long-memory dependence: assessing Ireland’s wind power resource. Appl Statist 38(1):1–50CrossRefGoogle Scholar
  15. Hosking JRM (1981) Fractional differencing. Biometrika 68:165–176MathSciNetzbMATHCrossRefGoogle Scholar
  16. Hsui, AT., Rust, K A., Klein, G D. (1993). A fractal analysis of Quaternary, Cenozoic- Mesozoic, and Late Pennsylvanian sea level changes. J Geophys Res 98 (B12), 21963–21967Google Scholar
  17. Hurst HE (1951) Long-term storage capacity of reservoirs. Trans Am Soc Civ Eng 116:77–779Google Scholar
  18. Koutsoyiannis D (2002) The hurst phenomenon and fractional Gaussian noise made easy. Hydrol Sci J 47(4):573–595CrossRefGoogle Scholar
  19. Koutsoyiannis D (2003) Climate change, the Hurst phenomenon, and hydrological statistics. Hydrol Sci J 48(1):3–27CrossRefGoogle Scholar
  20. Lo A (1991) Long-term memory in stock market prices. Econometrica 59:1279–1313zbMATHCrossRefGoogle Scholar
  21. Mandelbrot BB (1971) A fast fractional Gaussian noise generator. Water Resour Res 7(3):543–553CrossRefGoogle Scholar
  22. Mandelbrot BB, Van Ness JW (1968) Fractional Brownian motions, fractional noises and application. Soc Ind Appl Math Rev 10:422–437zbMATHGoogle Scholar
  23. Mandelbrot BB, Wallis JR (1968) Noah, Joseph and operational hydrology , Water Resour. Res. 4:909–920CrossRefGoogle Scholar
  24. Mandelbrot BB, Wallis JR (1969) Computer experiments with fractional Gaussian noises. Water Resour Res 5:228–267CrossRefGoogle Scholar
  25. Mandelbrot BB, Taqqu MS (1979) Robust R/S analysis of long run serial correlation. 42nd Session of the International Statistical Institute. Manila, Book 2:69–99MathSciNetGoogle Scholar
  26. Molz FJ, Boman GK (1993) A fractal-based stochastic interpolation scheme in subsurface hydrology. Water Resour Res 29(11):3769–3774CrossRefGoogle Scholar
  27. Montanari A, Rosso R, Taqqu MS (1997) Fractionally differenced ARIMA models applied to hvdrologic time series. Water Resour Res 33(5):1035–1044CrossRefGoogle Scholar
  28. Palma W (2007) Long-memory time series: theory and methods. Wiley, HobokenCrossRefGoogle Scholar
  29. Peng CK, Buldyrev SV, Havlin S, Simons M, Stanley HE, Goldberger AL (1994) Mosaic organization of DNA nucleotides. Phys Rev E 49:1685–1689CrossRefGoogle Scholar
  30. Stephenson, D B.,Pavan, V., Bojariu, R (2000). Is the North Atlantic Oscillation a random walk? Int J Clim 20(1), 1-18Google Scholar
  31. Taqqu, M.S., Teverovsky, V., Willinger, W. (1995). Estimators for long-range dependence: An empirical study. Fractals 3(4), 785-798Google Scholar
  32. Vogel RM, Tsai Y, Limbrunner JF (1998) The regional persistence and variability of annual streamflow in the United States. Water Resour Res 34(12):3445–3459CrossRefGoogle Scholar
  33. Vyushin DI, Kushner PJ (2009) Power-law and long-memory characteristics of the atmospheric general circulation. J Clim 22(11):2890–2904CrossRefGoogle Scholar
  34. Whittle P (1951) Hypothesis testing in time series analysis. Hafner, New YorkGoogle Scholar

Copyright information

© The Author(s) 2013

Authors and Affiliations

  • Ali Ercan
    • 1
    Email author
  • M. Levent Kavvas
    • 1
  • Rovshan K. Abbasov
    • 2
  1. 1.Department of Civil and Environmental EngineeringUniversity of CaliforniaDavisUSA
  2. 2.Khazar UniversityBakuAzerbaijan

Personalised recommendations