Long Memory Time Series

  • Jürgen FrankeEmail author
  • 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. Such series are reported to be characterised by distinct, but non periodic, cyclical patterns and their behaviour is such that current values are not only influenced by immediate past values but values from previous time periods. The terminology associated with a series with such characteristics is “long memory” or “long range dependence”. If financial time series exhibit persistence or long-memory, then their unconditional probability distribution may not be normal. This has important implications for many areas in finance, especially asset pricing, option pricing, portfolio allocation and risk management.


Fractional Brownian Motion Hurst Exponent Conditional Volatility Range Dependence Memory Parameter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Jürgen Franke
    • 1
    Email author
  • Wolfgang Karl Härdle
    • 2
    • 3
  • Christian Matthias Hafner
    • 4
  1. 1.FB MathematikTU KaiserslauternKaiserslauternGermany
  2. 2.Ladislaus von Bortkiewicz Chair of Statistics C.A.S.E. Centre for Applied Statistics and Economics School of Business and EconomicsHumboldt-Universität zu BerlinBerlinGermany
  3. 3.Graduate Institute of StatisticsNational Central UniversityJhongliTaiwan
  4. 4.Inst. StatistiqueUniversité Catholique de LouvainLeuven-la-NeuveBelgium

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