Eur. Phys. J. Plus (2021) 136: 105
https://doi.org/10.1140/epjp/s13360-021-01105-8

Regular Article

Detecting nonlinearity in the light curves of active galactic nuclei

¹ Tokyo University of Science, 102-0071, Fujimi, Chiyoda, Tokyo, Japan
² National Astronomical Observatory of Japan, 181-8588, Osawa, Mitaka, Tokyo, Japan

^a shoji@rs.tus.ac.jp

Received: 13 October 2020
Accepted: 11 January 2021
Published online: 19 January 2021

Abstract

This paper discusses a statistical method of detecting nonlinearity in the light curves of active galactic nuclei (AGN). We model the light curves of AGN by two-variate stochastic differential equation (SDE) in which one variable is observable but not the other. Applying a nonparametric model of the SDE as well as its parametric models of linear and quadratic functions to the light curves provided by the Kepler satellite, we estimate the three models and thereby compare their prediction accuracy to detect nonlinearity. The results suggest that there exist quadratic or other nonlinearities in the light curves, while the others exhibit linearity.