Multifractality in Time Series

Details Multifractality in Time Series Multifractality in Time Series

2000-04-11

arxiv.org/abs/cond-mat/0004170v1

Physics

Condensed Matter

22 pages, Revtex, 4 ps figures - To appear J. Phys. A (2000)

Scientific paper

10.1088/0305-4470/33/19/302

We apply the concepts of multifractal physics to financial time series in order to characterize the onset of crash for the Standard & Poor's 500 stock index x(t). It is found that within the framework of multifractality, the "analogous" specific heat of the S&P500 discrete price index displays a shoulder to the right of the main peak for low values of time lags. On decreasing T, the presence of the shoulder is a consequence of the peaked, temporal x(t+T)-x(t) fluctuations in this regime. For large time lags (T>80), we have found that C_{q} displays typical features of a classical phase transition at a critical point. An example of such dynamic phase transition in a simple economic model system, based on a mapping with multifractality phenomena in random multiplicative processes, is also presented by applying former results obtained with a continuous probability theory for describing scaling measures.

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