Novel SIMEX algorithm for autoregressive models to estimate AGN variability

The origin of the variability in accretion discs of active galactic nuclei (AGNs) is still unknown, but its behaviour can be characterized by modelling the time series of optical wavelength fluxes with damped random walk (DRW) being the most popular model for this purpose. The DRW depends on a fluctuation amplitude σ and damping time-scale τ, the latter potentially related to the mass and accretion rate on to the massive black hole. Estimating τ is challenging. Popular methods such as maximum likelihood (ML) and least-square error (LSE) result in biased estimators. This bias typically arises due to: (i) light curve observed with additive noise, (ii) the cadence scheme, and/or (iii) autocorrelation parameter near one – the so-called unit root problem, a known statistical challenge. To improve the estimation procedures for τ, we developed a simulation-extrapolation (SIMEX) methodology in the context of time series analysis. We applied it to both a standard autoregressive process (regular time intervals) and a recently developed irregularly autoregressive process (iAR). Its performance was evaluated under near-unit-root behaviour and additive noise via Monte Carlo simulations. This methodology was also tested in AGN light curves from the Zwicky Transient Facility survey, assessing its accuracy in estimating τ. Simulation results confirm that the SIMEX approach outperforms ML and LSE methods, reducing estimation bias by 30 per cent to 90 per cent. Real-data applications validate the methodology, yielding better fits and lower mean squared errors. A more accurate estimation of τ can contribute to understanding the links between DRW parameters and physical characteristics of AGN.