Parameter estimation from time-series data with correlated errors: A wavelet-based method and its application to transit light curves

Joshua A. Carter, Joshua N. Winn

Research output: Contribution to journalArticle

201 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)51-67
Number of pages17
JournalAstrophysical Journal
Volume704
Issue number1
DOIs
StatePublished - Jan 1 2009
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics
  • Space and Planetary Science

Keywords

  • Methods: statistical
  • Planetary systems
  • Techniques: photometric

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