Nested Sampling for ARIMA Model Selection in Astronomical Time-Series Analysis

The upcoming era of large-scale, high-cadence astronomical surveys demands efficient and robust methods for time-series analysis. ARIMA models provide a versatile parametric description of stochastic variability in this context. However, their practical use is limited by the challenge of selecting optimal model orders while avoiding overfitting. We present a novel solution to this problem using a Bayesian framework for time-series modelling in astronomy by combining Autoregressive Integrated Moving Average (ARIMA) models with the Nested Sampling algorithm. Our method yields Bayesian evidences for model comparison and also incorporates an intrinsic Occam's penalty for unnecessary model complexity. A vectorized ARIMA-Nested Sampling framework with GPU-acceleration support is implemented, allowing us to perform model selection across grids of Autoregressive (AR) and Moving Average (MA) orders, with efficient inference of selected model parameters. We validate the approach using simulated time series with known ground-truth parameters and demonstrate accurate recovery of both model order and parameters. We then apply the method to several astronomical datasets, including the historical sunspot number record, stellar light curves of KIC 12008916 and Kepler 17 from the Kepler mission, and quasar light curves of 3C 273 and S4 0954+65 from the TESS mission. In all cases, the ARIMA models selected by this method were able to accurately model the stochastic variability in the time series data. Our results demonstrate that nested sampling offers a rigorous and computationally tractable alternative to autoregressive model selection in astronomical time-series analysis.