A model for interevent times with long tails and multifractality in human communications: An application to financial trading

@misc{perello08, abstract = {Social, technological and economic time series are divided by events which are usually assumed to be random albeit with some hierarchical structure. It is well known that the interevent statistics observed in these contexts differs from the Poissonian profile being long-tailed distributed with resting and active periods interwoven. Understanding mechanisms generating consistent statistics have become a central issue. The approach we present is taken from the Continuous Time Random Walk formalism and represents an analytical alternative to mechanisms of non-trivial priority that have been recently proposed. Our analysis also goes one step further by looking at the multifractal structure of the interevent times of human decisions. We here analyze the inter-transaction time intervals of several financial markets. We observe that empirics describes a subtle multifractal behavior. Our model explains this structure by taking the pausing-time density in the form of a superstatistics where the integral kernel quantifies the heterogeneous nature of the executed tasks. An stretched exponential kernel provides a multifractal profile valid for a certain limited range. A suggested heuristic analytical profile is capable of covering a broader region.}, author = {Perello, J. and Masoliver, J. and Kasprzak, A. and Kutner, R. }, citeulike-article-id = {2795099}, eprint = {0805.1353}, keywords = {human\_dynamics, power-laws}, month = {May}, posted-at = {2008-05-13 15:04:27}, priority = {2}, title = {A model for interevent times with long tails and multifractality in human communications: An application to financial trading}, url = {http://arxiv.org/abs/0805.1353}, year = {2008} }

TY - ELEC ID - perello08 L3 - citeulike-article-id:2795099 TI - A model for interevent times with long tails and multifractality in human communications: An application to financial trading N2 - Social, technological and economic time series are divided by events which are usually assumed to be random albeit with some hierarchical structure. It is well known that the interevent statistics observed in these contexts differs from the Poissonian profile being long-tailed distributed with resting and active periods interwoven. Understanding mechanisms generating consistent statistics have become a central issue. The approach we present is taken from the Continuous Time Random Walk formalism and represents an analytical alternative to mechanisms of non-trivial priority that have been recently proposed. Our analysis also goes one step further by looking at the multifractal structure of the interevent times of human decisions. We here analyze the inter-transaction time intervals of several financial markets. We observe that empirics describes a subtle multifractal behavior. Our model explains this structure by taking the pausing-time density in the form of a superstatistics where the integral kernel quantifies the heterogeneous nature of the executed tasks. An stretched exponential kernel provides a multifractal profile valid for a certain limited range. A suggested heuristic analytical profile is capable of covering a broader region. KW - human_dynamics KW - power-laws AU - Perello, J AU - Masoliver, J AU - Kasprzak, A AU - Kutner, R PY - 2008/May/09/ UR - http://arxiv.org/abs/0805.1353 ER -