Nested Sampling Algorithm Improves ARIMA Model Selection for Astronomical Time-Series Data
Researchers have developed a new method combining ARIMA models with Nested Sampling to automatically select optimal parameters for analyzing astronomical time series while avoiding overfitting. The approach uses Bayesian evidence calculations and includes a built-in penalty for unnecessary model complexity, implemented with GPU acceleration for efficiency. The method was validated on simulated data and applied to real astronomical datasets including sunspot records, stellar light curves from Kepler, and quasar observations from TESS.
A new preprint describes a computational framework that addresses a longstanding challenge in astronomical time-series analysis: selecting the optimal order parameters for ARIMA (Autoregressive Integrated Moving Average) models without overfitting. The authors combine ARIMA modeling with the Nested Sampling algorithm, a Bayesian inference technique that naturally incorporates an Occam's penalty favoring simpler models. The framework, implemented in JAX and Blackjax with GPU acceleration, enables efficient model selection across grids of parameter combinations. The researchers validated their approach using simulated time series with known ground-truth parameters, demonstrating accurate recovery of both model orders and parameters. They then applied the method to several real astronomical datasets: the historical sunspot number record, stellar light curves from the Kepler mission (KIC 12008916 and Kepler 17), and quasar light curves from TESS (3C 273 and S4 0954+65). The results show that the nested sampling approach successfully models stochastic variability and produces accurate multi-step forecasts, with successful performance on all tested datasets except Kepler 17.
What's missing
The paper does not discuss computational cost comparisons with traditional model selection methods (e.g., AIC, BIC) or provide runtime benchmarks. The reasons for the method's failure on Kepler 17 are not explained in the abstract. The paper does not address how the method scales to extremely large surveys or discuss limitations when ARIMA assumptions (stationarity, linearity) may be violated in real astronomical data.
What different sources said
- arXiv astro-phCenter
Nested Sampling for ARIMA Model Selection in Astronomical Time-Series Analysis
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