  The log returns of financial time series are usually modeled by means of the
stationary GARCH(1,1) stochastic process or its generalizations which can not
properly describe the nonstationary deterministic components of the original
series. We analyze the influence of deterministic trends on the GARCH(1,1)
parameters using Monte Carlo simulations. The statistical ensembles contain
numerically generated time series composed by GARCH(1,1) noise superposed on
deterministic trends. The GARCH(1,1) parameters characteristic for financial
time series longer than one year are not affected by the detrending errors. We
also show that if the ARCH coefficient is greater than the GARCH coefficient,
then the estimated GARCH(1,1) parameters depend on the number of monotonic
parts of the trend and on the ratio between the trend and the noise amplitudes.
