Abstract
We consider representative financial records (stocks and indices) on time scales between one minute and one day, as well as historical monthly data sets, and show that the distribution of the interoccurrence times between losses below a negative threshold , for fixed mean interoccurrence times in multiples of the corresponding time resolutions, can be described on all time scales by the same exponentials, . We propose that the asset- and time-scale-independent analytic form of can be regarded as an additional stylized fact of the financial markets and represents a nontrivial test for market models. We analyze the distribution as well as the autocorrelation of the interoccurrence times for three market models: (i) multiplicative random cascades, (ii) multifractal random walks, and (iii) the generalized autoregressive conditional heteroskedasticity [GARCH(1,1)] model. We find that only one of the considered models, the multifractal random walk model, approximately reproduces the -exponential form of and the power-law decay of .
1 More- Received 31 January 2014
DOI:https://doi.org/10.1103/PhysRevE.90.062809
©2014 American Physical Society