  The origin of the long-range memory in the non-equilibrium systems is still
an open problem as the phenomenon can be reproduced using models based on
Markov processes. In these cases a notion of spurious memory is introduced. A
good example of Markov processes with spurious memory is stochastic process
driven by a non-linear stochastic differential equation (SDE). This example is
at odds with models built using fractional Brownian motion (fBm). We analyze
differences between these two cases seeking to establish possible empirical
tests of the origin of the observed long-range memory. We investigate
probability density functions (PDFs) of burst and inter-burst duration in
numerically obtained time series and compare with the results of fBm. Our
analysis confirms that the characteristic feature of the processes described by
a one-dimensional SDE is the power-law exponent $3/2$ of the burst or
inter-burst duration PDF. This property of stochastic processes might be used
to detect spurious memory in various non-equilibrium systems, where observed
macroscopic behavior can be derived from the imitative interactions of agents.
