Open AccessIntroducing fractal dimension algorithms to calculate the Hurst exponent of financial time series
Author(s) -
M.A. Sánchez-Granero,
M. Fernández–Martínez,
Juan Evangelista Trinidad Segovia
Publication year - 2012
Publication title -
the european physical journal b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 130
eISSN - 1434-6036
pISSN - 1434-6028
DOI - 10.1140/epjb/e2012-20803-2
Subject(s) - hurst exponent , series (stratigraphy) , fractal , monte carlo method , algorithm , fractal dimension , dimension (graph theory) , finance , stock market , computer science , time series , mathematics , statistics , machine learning , economics , mathematical analysis , biology , horse , pure mathematics , paleontology
In this paper, three new algorithms are introduced in order to explore long memory in financial time series. They are based on a new concept of fractal dimension of a curve. A mathematical support is provided for each algorithm and its accuracy is tested for different length time series by Monte Carlo simulations. In particular, in the case of short length series, the introduced algorithms perform much better than the classical methods. Finally, an empirical application for some stock market indexes as well as some individual stocks is presented
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