Autoregressive Planet Search: Methodology

Abstract

The detection of periodic signals from transiting exoplanets is often impeded by extraneous aperiodic photometric variability, either intrinsic to the star or arising from the measurement process. Frequently, these variations are autocorrelated wherein later flux values are correlated with previous ones. In this work, we present the methodology of the Autoregessive Planet Search (ARPS) project which uses Autoregressive Integrated Moving Average (ARIMA) and related statistical models that treat a wide variety of stochastic processes, as well as nonstationarity, to improve detection of new planetary transits. Providing a time series is evenly spaced or can be placed on an evenly spaced grid with missing values, these low-dimensional parametric models can prove very effective. We introduce a planet-search algorithm to detect periodic transits in the residuals after the application of ARIMA models. Our matched-filter algorithm, the Transit Comb Filter (TCF), is closely related to the traditional Box-fitting Least Squares and provides an analogous periodogram. Finally, if a previously identified or simulated sample of planets is available, selected scalar features from different stages of the analysis -the original light curves, ARIMA fits, TCF periodograms, and folded light curves -can be collectively used with a multivariate classifier to identify promising candidates while efficiently rejecting false alarms. We use Random Forests for this task, in conjunction with Receiver Operating Characteristic (ROC) curves, to define discovery criteria for new, high fidelity planetary candidates. The ARPS methodology can be applied to both evenly spaced satellite light curves and densely cadenced ground-based photometric surveys.

Toward a New Paradigm in the Analysis of Asteroseismic Lightcurves

“…We have developed the MIARMA algorithm, based on auto-regressive, moving -average models, to maximize the recovery of the frequency content in harmonic analysis. This algorithm has allowed us to improve the asteroseismic studies based on the global behavior of the modes, as attested by different publications on the subject, even in the search for planetary transits (see e.g., Caceres et al, 2019;Handler et al, 2019;Stuhr et al, 2019). Thanks to this improvement our group has confirmed the presence of a low-order large separation and its proportionality to the stellar mean density (Suárez et al, 2014;García Hernández et al, 2015).…”

A comprehensive power spectral density analysis of astronomical time series I: the Fermi-LAT gamma-ray light curves of selected blazars

“…Seager & Mallén-Ornelas 2003;Bond et al 2004). A planet search algorithm utilizing ARIMA models has been already proven to be effective (Caceres et al 2019). Moreover, the locations in the A − T plane, estimated based on properly sampled datasets, could assist in detections of new extrasolar planets.…”

An irregularly spaced first-order moving average model

“…Time series data observed at irregularly spaced intervals arise often in fields as diverse as astronomy, climatology, economics, finance, medical sciences, geophysics; see for example ?, Muñoz et al (1992), Belcher et al (1994), ?, Hand (2008), Corduas and Piccolo (2008), Harvill et al (2013), Podgorski (2014), Babu and Mahabal (2016), Eyheramendy et al (2018), ?, Edelmann et al (2019), Caceres et al (2019), Elorrieta et al (2019), and Zhang (2020), among others. In particular, in the climatology context, Mudelsee (2014) points out that conventional time series analysis has largely ignored irregularly spaced structures that climate time series must take into account.…”