Long Memory Time Series

  • Jürgen Franke
  • Wolfgang Karl Härdle
  • Christian Matthias Hafner
Part of the Universitext book series (UTX)


Empirical studies involving economic variables such as price level, real output and nominal interest rates have been shown to exhibit some degree of persistence. Moreover, findings across several asset markets have revealed a high persistence of volatility shocks and that over sufficiently long periods of time the volatility is typically stationary with “mean-reverting” behaviour.


  1. Baillie, R. T. (1996). Long memory and fractional integration in econometrics. Journal of Econometrics, 73, 5–59.MathSciNetCrossRefGoogle Scholar
  2. Beran, J. (1994). Statistics for long-memory processes. monographs of statistics and applied probability, vol. 61. London: Chapman and Hall.zbMATHGoogle Scholar
  3. Chung, C. F. (2001). Estimating the fractionally integrated GARCH model. Working Paper, National Taïwan University.Google Scholar
  4. Davidson, J. (2004). Moment and memory properties of linear conditional heteroscedasticity models, and a new model. Journal of Business and Economic Statistics, 22, 16–19.MathSciNetCrossRefGoogle Scholar
  5. Diebold, F. X., & Inoue, A. (2001). Long memory and regime switching. Journal of Econometrics, 105, 131–159.MathSciNetCrossRefGoogle Scholar
  6. Ding, Z., Granger, C. W. J., & Engle, R. F. (1993). A long memory property of stock market returns and a new model. Journal of Empirical Finance, 1, 83–106.CrossRefGoogle Scholar
  7. Embrechts, P. (2002). Self-similar processes. Princeton and Oxford.Google Scholar
  8. Engle, R. F., & Bollerslev, T. P. (1986). Modelling the persistence of conditional variances. Econometric Reviews, 5, 1–50, 81–87.MathSciNetCrossRefGoogle Scholar
  9. Geweke, J., & Porter-Hudak, S. (1983). The estimation and application of long-memory time series models. Journal of Time Series Analysis, 4, 221–238.MathSciNetCrossRefGoogle Scholar
  10. Giraitis, L., Kokoszka, P., Leipus, R., & Teyssière, G. (2003). Rescaled variance and related tests for long memory in volatility and levels. Journal of Econometrics, 112, 265–294.MathSciNetCrossRefGoogle Scholar
  11. Hurst, H. E. (1951). Long-term storage capacity of reservoirs. Transactions of the American Society of Civil Engineers, 116, 770–799.Google Scholar
  12. Hurst, H. E. (1957). A suggested statistical model for some time series that occur in natur. Nature, 494(180).Google Scholar
  13. Hurvich, C., Deo, R., & Brodsky, J. (1998). The mean square error of Geweke and Porter-Hudak’s estimator of the memory parameter of a long-memory time series. Journal of Time Series Analysis, 19, 19–46.MathSciNetCrossRefGoogle Scholar
  14. Kim, C. S., & Phillips, P. C. B. (2006). Log periodogram regression in the nonstationary case. Cowles Foundation Discussion Paper, Yale University.Google Scholar
  15. Lobato, I., & Robinson, P. (1998). A nonparametric test for i(0). Review of Economic Studies, 3, 475–495.CrossRefGoogle Scholar
  16. Mandelbrot, B. (1977). Fractals: Form, chance and dimension. San Francisco, CA.zbMATHGoogle Scholar
  17. Mandelbrot, k., & Van Ness, J. (1968). Fractional Brownian motions, fractional noises and applications. SIAM Review, 10, 422–437.Google Scholar
  18. Newey, W. K., & West, K. D. (1987). A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica, 55(3), 703–708. Scholar
  19. Phillips, P. C. B., & Shimotsu, K. (2004). Local whittle estimation in nonstationary and unit root cases. Annals of Statistics, 32, 656–692.MathSciNetCrossRefGoogle Scholar
  20. Robinson, P. M. (1995a). Gaussian semiparametric estimation of long-range dependence. Annals of Statistics, 23, 1630–1661.MathSciNetCrossRefGoogle Scholar
  21. Robinson, P. M., & Henry, M. (1999). Long and short memory conditional heteroscedasticity in estimating the memory parameter in levels. Economic Theory, 15(299–336).Google Scholar
  22. Samorodnitsky, G., & Taqqu, M. (1994). Stable and non-Gaussian random processes. New York.zbMATHGoogle Scholar
  23. Shimotsu, K. (2006). Simple (but effective) tests of long memory versus structural breaks. Working paper, Queen’s Economics Department, Queen’s University, Ontario-Canada.Google Scholar
  24. Sowell, F. (1992). Maximum likelihood estimation of stationary univariate fractional integrated time series models. Journal of Econometrics, 53, 165–188.MathSciNetCrossRefGoogle Scholar
  25. Tse, Y. K. (1998). The conditional heteroscedasticity of the yen-dollar exchange rate. Journal of Applied Econometrics, 5, 49–55.CrossRefGoogle Scholar
  26. Velasco, C. (1999). Non-stationary log-periodogram regression. Journal of Econometrics, 91, 325–371.MathSciNetCrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Jürgen Franke
    • 1
  • Wolfgang Karl Härdle
    • 2
  • Christian Matthias Hafner
    • 3
  1. 1.Department of MathematicsTechnische Universität KaiserslauternKaiserslauternGermany
  2. 2.Ladislaus von Bortkiewicz Chair of StatisticsHumboldt-Universität BerlinBerlinGermany
  3. 3.Louvain Institute of Data Analysis and Modeling in Economics and StatisticsUCLouvainLouvain-la-NeuveBelgium

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