Parameter Estimation from Time-series Data with Correlated Errors: A Wavelet-based Method and its Application to Transit Light Curves
Abstract
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 γ. 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 mid-transit 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 mid-transit times and truer estimates of their uncertainties.
- Publication:
-
The Astrophysical Journal
- Pub Date:
- October 2009
- DOI:
- 10.1088/0004-637X/704/1/51
- arXiv:
- arXiv:0909.0747
- Bibcode:
- 2009ApJ...704...51C
- Keywords:
-
- methods: statistical;
- planetary systems;
- techniques: photometric;
- Astrophysics - Earth and Planetary Astrophysics;
- Physics - Data Analysis;
- Statistics and Probability
- E-Print:
- Accepted in ApJ. Illustrative code may be found at http://www.mit.edu/~carterja/code/ . 17 pages