We consider the impact of Doppler noise models on the statistical robustness of the exoplanetary radial-velocity fits .
We show that the traditional model of the Doppler noise with an additive jitter can generate large non-linearity effects , decreasing the reliability of the fit , especially in the cases when a correleated Doppler noise is involved .
We introduce a regularization of the additive noise model that can gracefully eliminate its singularities together with the associated non-linearity effects .

We apply this approach to Doppler time-series data of several exoplanetary systems .
It demonstrates that our new regularized noise model yields orbital fits that have either increased or at least the same statistical robustness , in comparison with the simple additive jitter .
Various statistical uncertainties in the parametric estimations are often reduced , while planet detection significance is often increased .

Concerning the 55 Cnc five-planet system , we show that its Doppler data contain significant correlated ( “ red ” ) noise .
Its correlation timescale is in the range from days to months , and its magnitude is much larger than the effect of the planetary N -body perturbations in the radial velocity ( these perturbations thus appear undetectable ) .
Characteristics of the red noise depend on the spectrograph/observatory , and also show a cyclic time variation in phase with the public Ca II H & K and photometry measurements .
We interpret this modulation as a hint of the long-term activity cycle of 55 Cnc , similar to the Solar 11-year cycle .
We estimate the 55 Cnc activity period by 12.6 \pm ^ { 2.5 } _ { 1.0 } yrs , with the nearest minimum presumably expected in 2014 or 2015 .