Novel SIMEX algorithm for autoregressive models to estimate AGN variability

Abstract

The origin of the variability in accretion disks of active galactic nuclei (AGN) is still unknown, but its behavior can be characterized by modeling the time series of optical wavelength fluxes coming from the accretion disks with damped random walk (DRW) being the most popular model for this purpose. The DRW is modeled by a characteristic fluctuation amplitude and damping timescale {\tau}, with the latter being potentially related to the mass and accretion rate onto the massive black hole. The estimation of {\tau} is challenging, with commonly used methods such as the maximum likelihood (ML) and the least square error (LSE) resulting in biased estimators. This problem arises most commonly for three reasons: i) the light curve has been observed with additive noise; ii) some cadence scheme; iii) when the autocorrelation parameter is close to one. The latter is called the unit root problem. In order to improve these parameter estimation procedures for estimating {\tau}, we developed a simulation-extrapolation (SIMEX) methodology in the context of time series analysis. We consider both the standard class of autoregressive processes observed at regular intervals and a recently developed class of irregularly autoregressive processes (iAR). The performance of the SIMEX estimation method was evaluated under conditions of near-unit-root behavior and additive noise through extensive Monte Carlo simulations. Monte Carlo experiments confirm that the SIMEX approach outperforms MLE and LSE methods, offering a reduction in estimation bias ranging from 30% to 90%. Real-data applications further validate the methodology, yielding better model fits and lower mean squared errors (MSE). The more accurate estimation of the damping timescale parameter can help to better understand the currently tentative links between DRW and physical parameters in AGN.