We consider the problem of fitting a parametric model to time-series data that are afflicted by correlated noise. The noise is represented by a sum of two stationary Gaussian processes: one that is uncorrelated in time, and another that has a power spectral density varying as $1/f^gamma$. We present an accurate and fast [O(N)] algorithm for parameter estimation based on computing the likelihood in a wavelet basis. The method is illustrated and tested using simulated time-series photometry of exoplanetary transits, with particular attention to estimating the midtransit time. We compare our method to two other methods that have been used in the literature, the time-averaging method and the residual-permutation method. For noise processes that obey our assumptions, the algorithm presented here gives more accurate results for midtransit times and truer estimates of their uncertainties.

k2photometry reads, reduces and detrends K2 photometry and searches for transiting planets. MAST database pixel files are used as input; the output includes raw lightcurves, detrended lightcurves and a transit search can be performed as well. Stellar variability is not typically well-preserved but parameters can be tweaked to change that. The BLS algorithm used to detect periodic events is a Python implementation by Ruth Angus and Dan Foreman-Mackey (https://github.com/dfm/python-bls).