Microscopic Reasoning For The Non-linear Stochastic Models Of Long-range Memory
The authors extend Kirman's model by introducing variable event time scale. The proposed flexible time scale is equivalent to the variable trading activity observed in financial markets. Stochastic version of the extended Kirman's agent based model is compared to the non-linear stochastic model of long-range memory in financial markets. Agent based model providing matching macroscopic description serves as a microscopic reasoning of the earlier proposed stochastic model exhibiting power law statistics. Computational modeling of complex systems has become a rapidly developing method of doing science. This approach is indispensable when microscopic nature of interactions is unambiguously de fined. Nevertheless in the prevailing majority of social systems microscopic nature of interactions has to be deduced from the macroscopic behavior of the whole system.