Journal of Statistical Physics

, Volume 164, Issue 2, pp 438–448 | Cite as

Discretization of Continuous Time Discrete Scale Invariant Processes: Estimation and Spectra



Imposing some flexible sampling scheme we provide some discretization of continuous time discrete scale invariant (DSI) processes which is a subsidiary discrete time DSI process. Then by introducing some simple random measure we provide a second continuous time DSI process which provides a proper approximation of the first one. This enables us to provide a bilateral relation between covariance functions of the subsidiary process and the new continuous time processes. The time varying spectral representation of such continuous time DSI process is characterized, and its spectrum is estimated. Also, a new method for estimation time dependent Hurst parameter of such processes is provided which gives a more accurate estimation. The performance of this estimation method is studied via simulation. Finally this method is applied to the real data of S & P500 and Dow Jones indices for some special periods.


Discretization of continuous time DSI processes Time dependent Hurst parameter estimation Spectral representation 

Mathematics Subject Classification

60G18 60G99 


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Faculty of Mathematics and Computer ScienceAmirkabir University of TechnologyTehranIran
  2. 2.Faculty of MathematicsAlzahra UniversityTehranIran

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