Apparent multifractality in financial time series

European Physical Journal B

Volumn 13, Issue 3, 2000, Pages 595-599

  Bouchaud, J P ^a,b   Potters, M ^a   Meyer, M ^a  

^a Science and Finance   (France)

^b SERVICE DE PHYSIQUE DE L ETAT CONDENSÉ   (France)

Author keywords

02.50. r Probability theory, stochastic processes, and statistics; 05.40. a Fluctuation phenomena, random processes, noise, and Brownian motion; 89.90.+n Other topics of general interest to physicists (restricted to new topics in section 8)

Indexed keywords

EID: 0000953234     PISSN: 14346028     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

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34. One could also choose a non zero mean value for σ and not take the absolute value. This would still lead to an soluble model.
35. The (time-domain) correlation function defined by this construction explicitly depends on the number of variables in the sum N. This is not a problem when v > 0, since when N is large, this correlation function is equal to a well-defined N-independent limit plus sub-leading correction which can be safely neglected. Therefore, any subpart of the series of size n such that 1 ≪ n ≪ N will behave, as a function of n, as the whole sum.
36. i can take two values ±1. The model considered would then be tantamount to the Ising model in one dimension with long-ranged correlations.
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40. The case where the volatility is the exponential of a random walk is also soluble, and has been worked out by A. Matacz (unpublished).
41. 2, which interpolate between a Gaussian and a symmetric exponential.