We obtain a convincing fit to the observed X-ray lightcurve of an AGN using a LSSM AR[1] process as well in the time and in the frequency domain. The explicit modelling of observational noise allows to estimate the covered AR[1] process, indicating that the stochastic process is dominated by a single relaxation timescale. We show that the general AR[p] model (see Eq. 1) can be restricted to a simple AR[1] process which succeeds in describing the entire dynamics of the observed AGN X-ray lightcurve.
It has been suggested by McHardy (1988) that the single shots, which are supposed to be superimposed to build the lightcurve, may arise from subregions of an overall larger chaotic region which are temporarily lit up, perhaps by shocks. Since one would expect a non uniform electron density throughout this region (probably decreasing with distance from the central engine), the resulting difference in cooling timescales yields the different decay timescales (Green et al. 1993). As the LSSM predicts that the stochastic process is dominated by a single relaxator, we presume the existence of a single cooling timescale or a uniform electron density in the emission region following the shot noise model (see Sutherland et al. 1978).
The assumption of an exponentially decaying shot seems to be reasonable as
time-dependent Comptonisation models lead to such a pulse profile. The
scenario for a thermal Comptonisation model (Payne 1980;
Liang & Nolan 1983) starts with UV photons which arise as the
accretion inflows inhomogeneities, each producing a single flare when
gravitational energy is set free as radiation. The impulsive emission of the
Poisson distributed delta peaks in a cloud of hot electrons triggers X-ray
flares with a specific pulse profile depending on the seed photon energy,
the density, and the temperature of the electrons. This impulsive emission
is delayed and broadened in time and spectrally hardened due to repeated
Compton scattering. Some approximate analytic solutions of this process show
that the temporal evolution of the generated X-ray pulse can be described by
a nearly exponentially decaying function (Miyamoto & Kitamoto
1989). The only difference to the "shots" used above is the (more
realistic) non-zero rise time. Using this model it should be possible to
associate the estimated relaxator timescale 
with the
physical properties of the Comptonisation process.
The presented LSSM can also be used to analyse X-ray variability of galactic X-ray sources. As both, relaxators and (damped) oscillators can be estimated, it is possible to use the algorithm to search for periodocities and QPO phenomena in the lightcurves of X-ray binaries (see Robinson & Nather 1979; Lewin et al. 1988; van der Klis 1989).
Acknowledgements
We would like to thank J.D. Scargle, R. Staubert, M. Maisack, J. Wilms and K. Pottschmidt for helpful discussions and C. Gantert for writing the code of the LSSM program. Furthermore, we thank the anonymous referee for constructive comments.