Nonlinear time series analysis of Kepler Space Telescope data: Mutually beneficial progress

Nonlinear time series analysis, though a powerful tool, has not been used widely in astronomy and astro‐physics because the principle requirements that the data be sampled uniformly and continuous are rarely met. Kepler Space Telescope variable‐star light curves satisfy these and almost all other requirements. These data have allowed a more systematic study of the methodology and yielded new information. Nonlinear noise reduction is the aspect we focus on here. Nonlinear time series power spectra often have relevant information across all the frequencies in a spectrum. As opposed to traditional filtering that results in a loss of information at the high frequencies, nonlinear local projective noise reduction allows us to significantly reduce noise while keeping high‐frequency information. Nonlinear noise reduction is discussed for a number of Kepler Space Telescope targets with different power‐spectral characteristics. The extremely high quality of the Kepler data has also allowed us to explore the novel use of average mutual information (AMI) for distinguishing signal from noise in broadband spectra. We report on noise reduction for targets with power spectra that contain a fundamental and harmonics, power spectra with no such lines and spectra with high‐frequency lines (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)