# Autoregressive Times Series Methods for Time Domain Astronomy

**Authors:** Eric D. Feigelson, G. Jogesh Babu, Gabriel A. Caceres  
**arXiv:** [1901.08003](https://arxiv.org/abs/1901.08003)  
**Date:** 2019-01-23  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/1901.08003v1/

## Key points

- Authors explore application of parametric autoregressive modeling to interpret astronomical light curves
- Underutilization of this approach in astronomy despite common use in statistics
- Review of standard ARMA, ARIMA, and ARFIMA models addressing short-memory autocorrelation, long-memory red noise, and nonstationary trends
- Adaptation of models to handle irregular cadences by treating them as evenly spaced with missing data
- Emphasis on efficiency of fitting algorithms and availability of software implementations for these models
- Application of ARIMA models to analyze light curves from four variable stars and evaluation of effectiveness in capturing different temporal characteristics
- Outline extensions to ARIMA with focus on continuous-time models like CARMA and CARFIMA for irregularly spaced time series
- Discussion on strengths and weaknesses of ARIMA-type modeling for analyzing astronomical data and extracting astrophysical insights

## Summary

In their paper "Autoregressive Times Series Methods for Time Domain Astronomy," authors Eric D. Feigelson, G. Jogesh Babu, and Gabriel A. Caceres explore the application of parametric autoregressive modeling to interpret astronomical light curves. They highlight the underutilization of this approach in astronomy despite its common use in statistics. The study reviews standard ARMA, ARIMA, and ARFIMA models that address various aspects of time series data such as short-memory autocorrelation, long-memory red noise, and nonstationary trends. The authors discuss how these models can be adapted to handle moderately irregular cadences by treating them as evenly spaced with missing data. They also emphasize the efficiency of fitting algorithms and the widespread availability of software implementations for these models. The researchers apply ARIMA models to analyze light curves from four variable stars and evaluate their effectiveness in capturing different temporal characteristics. They also outline extensions to ARIMA, focusing on continuous-time models like CARMA and CARFIMA specifically developed for irregularly spaced time series. Furthermore, the paper delves into the strengths and weaknesses of ARIMA-type modeling for analyzing astronomical data and extracting astrophysical insights. By bridging statistical methods with astronomical research, this study sheds light on the potential benefits of incorporating parametric autoregressive modeling into the analysis of celestial variability.