PARAMETER ESTIMATION FROM TIME-SERIES DATA WITH CORRELATED ERRORS: A WAVELET-BASED METHOD AND ITS APPLICATION TO TRANSIT LIGHT CURVES
Author(s)Carter, Joshua Adam; Winn, Joshua Nathan
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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 [superscript 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.
DepartmentMassachusetts Institute of Technology. Department of Physics; MIT Kavli Institute for Astrophysics and Space Research
American Astronomical Society
Carter, Joshua A. and Joshua N. Winn "Parameter Estimation from Time-series Data with Correlated Errors: A Wavelet-based Method and its Application to Transit Light Curves." 2009 ApJ 704 51-67 doi: 10.1088/0004-637X/704/1/51
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