Effective temperature of self-similar time series

Abstract

Within slightly non-extensive statistics and the related numerical model, a picture is elaborated to treat self-similar time series as a thermodynamic system. Thermodynamic-type characteristics relevant to temperature, pressure, entropy, internal and free energies are introduced and tested. The statistics developed is shown to be governed by the effective temperature being exponential measure of the fractal dimension of the time series. Testing of the analytical consideration is based on the numerical scheme of non-extensive random walk. Effective temperature is found numerically to show that its value is reduced to averaged energy per one degree of freedom.