  We address the problem of long-range memory in the financial markets. There
are two conceptually different ways to reproduce power-law decay of
auto-correlation function: using fractional Brownian motion as well as
non-linear stochastic differential equations. In this contribution we address
this problem by analyzing empirical return and trading activity time series
from the Forex. From the empirical time series we obtain probability density
functions of burst and inter-burst duration. Our analysis reveals that the
power-law exponents of the obtained probability density functions are close to
$3/2$, which is a characteristic feature of the one-dimensional stochastic
processes. This is in a good agreement with earlier proposed model of absolute
return based on the non-linear stochastic differential equations derived from
the agent-based herding model.
