widths are taken small enough to allow only weak fluctuations ($\approx 10\%$) around the mean values.

Adding new fit parameters allows us to determine $h_f$ in more and more detail and improves the convergence of the autocorrelation function of the model dynamical system to the given (experimental) autocorrelation function. Indeed, as we shall see below, only a few elements $h_{f,i}$ are required to achieve a rather good convergence. In the next section we give some examples demonstrating how the above-described method can be applied to construct a (piecewise) smooth map simulating a system with given time correlations.

Numerical examples and discussion
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Before turning to the examples and results of our computational method let us provide some additional aspects concerning the determination of the correlation function. We restrict our investigations to a rather small set of values for the correlation function $C(n)$, more precisely to the set $\{C(0),...,C(5)\}$. The reason for this restriction is that the exact calculation of the correlation function which has to be accomplished for each single step of the Monte-Carlo scheme is computationally very intensive (see below, the total amount of CPU of our calculations on a powerful workstation was approximately three months). The reliable evaluation 