# Autoregressive Times Series Methods for Time Domain Astronomy

## TL;DR

This paper reviews autoregressive models like ARIMA and their extensions for analyzing astronomical light curves, highlighting their effectiveness, limitations, and recent continuous-time developments for irregularly spaced data.

## Contribution

It provides a comprehensive review of ARIMA and related models tailored for astronomical time series, including recent continuous-time models for irregular data.

## Key findings

- ARIMA models are effective for certain types of astronomical light curves.
- Extensions like CARMA and CARFIMA address irregular sampling issues.
- The paper discusses strengths and limitations of autoregressive methods in astronomy.

## Abstract

Celestial objects exhibit a wide range of variability in brightness at different wavebands. Surprisingly, the most common methods for characterizing time series in statistics -- parametric autoregressive modeling -- is rarely used to interpret astronomical light curves. We review standard ARMA, ARIMA and ARFIMA (autoregressive moving average fractionally integrated) models that treat short-memory autocorrelation, long-memory $1/f^\alpha$ `red noise', and nonstationary trends. Though designed for evenly spaced time series, moderately irregular cadences can be treated as evenly-spaced time series with missing data. Fitting algorithms are efficient and software implementations are widely available. We apply ARIMA models to light curves of four variable stars, discussing their effectiveness for different temporal characteristics. A variety of extensions to ARIMA are outlined, with emphasis on recently developed continuous-time models like CARMA and CARFIMA designed for irregularly spaced time series. Strengths and weakness of ARIMA-type modeling for astronomical data analysis and astrophysical insights are reviewed.