  Stellar photometric variability and instrumental effects, like cosmic ray
hits, data discontinuities, data leaks, instrument aging etc. cause
difficulties in the characterization of exoplanets and have an impact on the
accuracy and precision of the modelling and detectability of transits,
occultations and phase curves. This paper aims to make an attempt to improve
the transit, occultation and phase-curve modelling in the presence of strong
stellar variability and instrumental noise. We invoke the wavelet-formulation
to reach this goal. We explore the capabilities of the software package Transit
and Light Curve Modeller (TLCM). It is able to perform a joint radial velocity
and light curve fit or light curve fit only. It models the transit,
occultation, beaming, ellipsoidal and reflection effects in the light curves
(including the gravity darkening effect, too). The red-noise, the stellar
variability and instrumental effects are modelled via wavelets. The wavelet-fit
is constrained by prescribing that the final white noise level must be equal to
the average of the uncertainties of the photometric data points. This helps to
avoid the overfit and regularizes the noise model. The approach was tested by
injecting synthetic light curves into Kepler's short cadence data and then
modelling them. The method performs well over a certain signal-to-noise (S/N)
ratio. In general a S/N ratio of 10 is needed to get good results but some
parameters requires larger S/N, some others can be retrieved at lower S/Ns. We
give limits in terms of signal-to-noise ratio for every studied system
parameter which is needed to accurate parameter retrieval. The wavelet-approach
is able to manage and to remove the impacts of data discontinuities, cosmic ray
events, long-term stellar variability and instrument ageing, short term stellar
variability and pulsation and flares among others. (...)
