Bayesian ARIMA model selection for astronomical time-series analysis using Nested Sampling.

NestAR combines Nested Sampling with ARIMA (AutoRegressive Integrated Moving Average) models for Bayesian model selection.

It provides a rigorous alternative to maximum-likelihood based selection and fitting of ARIMA models, such as using the Bayesian or Akaike Information Criterion.

For a selected model, NestAR also provides posterior samples, model reconstruction, and posterior-based forecasting.

The nested-sampling implementation uses BlackJAX, with JAX providing the numerical backend.

Clone the repository:

git clone https://github.com/najinkya1313/NestAR.git
cd NestAR

Install NestAR and its dependencies:

python -m pip install .

For development:

python -m pip install -e .

Fit a single ARIMA model using Nested Sampling:

from nestar.ARIMA_ns import ARIMA_Nested_Sampler

model = ARIMA_Nested_Sampler(
    data=your_time_series,
    order=(1, 0, 1),
    mu_mean=0,
    mu_scale=1,
    num_live=500,
    num_delete=50,
    seed=42,
)

model.summary()

Full documentation, including the API reference, examples, and detailed usage information, is available at:

NestAR Documentation

If you use NestAR in your research or work, please cite the accompanying paper:

A. J. Naik & W. Handley, Nested Sampling for ARIMA Model Selection in Astronomical Time-Series Analysis.

arXiv:2512.01929

@article{naik2025nestar,
  title         = {Nested Sampling for ARIMA Model Selection in Astronomical Time-Series Analysis},
  author        = {Naik, Ajinkya and Handley, Will},
  journal       = {arXiv preprint arXiv:2512.01929},
  year          = {2025},
  eprint        = {2512.01929},
  archivePrefix = {arXiv}
}

NestAR is released under the MIT License. See LICENSE for details.