  Time-correlated noise is a significant source of uncertainty when modeling
exoplanet light-curve data. A correct assessment of correlated noise is
fundamental to determine the true statistical significance of our findings.
Here we review three of the most widely used correlated-noise estimators in the
exoplanet field, the time-averaging, residual-permutation, and
wavelet-likelihood methods. We argue that the residual-permutation method is
unsound in estimating the uncertainty of parameter estimates. We thus recommend
to refrain from this method altogether. We characterize the behavior of the
time averaging's rms-vs.-bin-size curves at bin sizes similar to the total
observation duration, which may lead to underestimated uncertainties. For the
wavelet-likelihood method, we note errors in the published equations and
provide a list of corrections. We further assess the performance of these
techniques by injecting and retrieving eclipse signals into synthetic and real
Spitzer light curves, analyzing the results in terms of the relative-accuracy
and coverage-fraction statistics. Both the time-averaging and
wavelet-likelihood methods significantly improve the estimate of the eclipse
depth over a white-noise analysis (a Markov-chain Monte Carlo exploration
assuming uncorrelated noise). However, the corrections are not perfect, when
retrieving the eclipse depth from Spitzer datasets, these methods covered the
true (injected) depth within the 68\% credible region in only $\sim$45--65\% of
the trials. Lastly, we present our open-source model-fitting tool, Multi-Core
Markov-Chain Monte Carlo ({MC$^3$}). This package uses Bayesian statistics to
estimate the best-fitting values and the credible regions for the parameters
for a (user-provided) model. {MC$^3$} is a Python/C code, available at
https://github.com/pcubillos/MCcubed.
