On the Use of Stochastic Complexity in Spectral Analysis of Radial Velocity Data

Abstract

The periodogram and its variants have been extensively used in the past for estimating the power spectral density. In this book chapter, we consider the case when the measurements are not equidistantly spaced on the time-axis, and we focus on testing the significance of the periodogram peaks. Because it is known that the standard tests of hypothesis testing are not suitable for this problem, we propose the use of Stochastic Complexity (SC). The performance of SC is evaluated in comparison with the Bayesian Information Criterion (BIC), which has been employed in the previous literature to solve the same problem. The numerical experiments on radial velocity measurements demonstrate that SC compares favorably with BIC.