TY - JOUR

T1 - Discrete-time autoregressive model for unequally spaced time-series observations

AU - Elorrieta, Felipe

AU - Eyheramendy, Susana

AU - Palma, Wilfredo

N1 - Funding Information:
Acknowledgements. Support for this research was provided by grant IC120009, awarded to The Millennium Institute of Astrophysics, MAS, and from Fondecyt grant 1160861. F.E. acknowledges support from CONICYT-PCHA (Doctorado Nacional 2014-21140566).
Funding Information:
Support for this research was provided by grant IC120009, awarded to The Millennium Institute of Astrophysics, MAS, and from Fondecyt grant 1160861. F.E. acknowledges support from CONICYT-PCHA (Doctorado Nacional 2014- 21140566).
Publisher Copyright:
© ESO 2019.

PY - 2019/7/1

Y1 - 2019/7/1

N2 - Most time-series models assume that the data come from observations that are equally spaced in time. However, this assumption does not hold in many diverse scientific fields, such as astronomy, finance, and climatology, among others. There are some techniques that fit unequally spaced time series, such as the continuous-time autoregressive moving average (CARMA) processes. These models are defined as the solution of a stochastic differential equation. It is not uncommon in astronomical time series, that the time gaps between observations are large. Therefore, an alternative suitable approach to modeling astronomical time series with large gaps between observations should be based on the solution of a difference equation of a discrete process. In this work we propose a novel model to fit irregular time series called the complex irregular autoregressive (CIAR) model that is represented directly as a discrete-time process. We show that the model is weakly stationary and that it can be represented as a state-space system, allowing efficient maximum likelihood estimation based on the Kalman recursions. Furthermore, we show via Monte Carlo simulations that the finite sample performance of the parameter estimation is accurate. The proposed methodology is applied to light curves from periodic variable stars, illustrating how the model can be implemented to detect poor adjustment of the harmonic model. This can occur when the period has not been accurately estimated or when the variable stars are multiperiodic. Last, we show how the CIAR model, through its state space representation, allows unobserved measurements to be forecast.

AB - Most time-series models assume that the data come from observations that are equally spaced in time. However, this assumption does not hold in many diverse scientific fields, such as astronomy, finance, and climatology, among others. There are some techniques that fit unequally spaced time series, such as the continuous-time autoregressive moving average (CARMA) processes. These models are defined as the solution of a stochastic differential equation. It is not uncommon in astronomical time series, that the time gaps between observations are large. Therefore, an alternative suitable approach to modeling astronomical time series with large gaps between observations should be based on the solution of a difference equation of a discrete process. In this work we propose a novel model to fit irregular time series called the complex irregular autoregressive (CIAR) model that is represented directly as a discrete-time process. We show that the model is weakly stationary and that it can be represented as a state-space system, allowing efficient maximum likelihood estimation based on the Kalman recursions. Furthermore, we show via Monte Carlo simulations that the finite sample performance of the parameter estimation is accurate. The proposed methodology is applied to light curves from periodic variable stars, illustrating how the model can be implemented to detect poor adjustment of the harmonic model. This can occur when the period has not been accurately estimated or when the variable stars are multiperiodic. Last, we show how the CIAR model, through its state space representation, allows unobserved measurements to be forecast.

KW - Methods: data analysis

KW - Methods: statistical

KW - Stars: general

UR - http://www.scopus.com/inward/record.url?scp=85069467451&partnerID=8YFLogxK

U2 - 10.1051/0004-6361/201935560

DO - 10.1051/0004-6361/201935560

M3 - Article

AN - SCOPUS:85069467451

SN - 0004-6361

VL - 627

JO - Astronomy and Astrophysics

JF - Astronomy and Astrophysics

M1 - A120

ER -