It is a good start if you could observe it from FRACTAL scope.

I suggest you to have a look at the econometrics works with 'long memory' in the keyword list. Moreover, you could have a look at works published by Dacorogna and co-authors from 1995 onwards and at the book by Beran on long-memory time series

@Setyawan, Sami and Mr. Caporin: Thanks, I am checking them out.

These first two papers identify "unusual", which might be the opposite of what you asked for -

Downing, D. J., et al. "Large Data Sets: Segmentation, Feature Extraction and Compression." Document ORNL-13114, Computer Science and Mathematics Division, Mathematical Sciences Section, Oak Ridge National Laboratory, Oak Ridge, Tennessee (1996).

Downing, D. J., et al. Analysing Perturbations and Nonstationarity in Data Series using Techniques Motivated by the Theory of Chaotic Nonlinear Dynamical Systems. No. ORNL/TM--13115. Oak Ridge National Lab., TN (United States), 1996.

As far as "repetition" goes, perhaps -

Gaffney, Scott, and Padhraic Smyth. "Trajectory clustering with mixtures of regression models." Proceedings of the fifth ACM SIGKDD international conference on Knowledge discovery and data mining. ACM, 1999.

I know these references are old, but I haven't looked into this problem in a while.

Mr. Lai

I'm having a similar doubt and I think the following paper regarding Hurst exponent estimators might help you as well :

"Estimators for Long Range Dependence: An Empirical Study" , William et al. 2009

It uses the fSeries package in R, which has helped me a lot.

Best Regards

http://arxiv.org/pdf/0901.0762.pdf