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arxiv: 2604.16719 · v1 · submitted 2026-04-17 · 💻 cs.LG

Chronax: A Jax Library for Univariate Statistical Forecasting and Conformal Inference

Xan Carey , Yash Deshmukh , Aileen Huang , Sunit Jadhav , Omkar Tekawade , Lorraine Yang , Anvesha Tiwary , Gerardo Riano
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Amy Greenwald Denizalp Goktas
This is my paper

Pith reviewed 2026-05-10 08:12 UTC · model grok-4.3

classification 💻 cs.LG
keywords time-series forecastingJAX libraryconformal inferenceunivariate modelsaccelerator executionuncertainty quantificationmulti-series datafunctional transformations
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The pith

Chronax represents time-series forecasting steps as pure JAX functions to enable scalable multi-series predictions with conformal uncertainty estimates.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces Chronax, a library for univariate statistical forecasting built natively in JAX. It treats preprocessing, modeling, and multi-horizon prediction as pure functions that support just-in-time compilation and automatic vectorization. This setup targets large collections of time series that need frequent retraining and irregular covariates. A sympathetic reader would care because traditional Python forecasting tools face limits in parallelism and integration with accelerator hardware or differentiable workflows. If the design holds, it would allow forecasting systems to run more efficiently across CPUs, GPUs, and TPUs while adding model-agnostic ways to quantify uncertainty.

Core claim

By representing preprocessing, modeling, and multi-horizon prediction as pure JAX functions, Chronax enables scalable multi-series forecasting, model-agnostic conformal uncertainty quantification, and seamless integration with modern machine learning and scientific computing pipelines.

What carries the argument

Pure JAX functions that wrap forecasting operations and permit program transformations such as compilation and vectorization for end-to-end accelerator execution.

If this is right

  • Large collections of heterogeneous time series can be forecasted at scale through automatic vectorization.
  • Conformal uncertainty estimates apply across different models without model-specific adjustments.
  • Forecasting pipelines integrate directly into JAX-based differentiable and accelerator workflows.
  • Execution becomes efficient on CPUs, GPUs, and TPUs via built-in program transformations.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar functional designs could apply to other statistical tasks that benefit from hardware acceleration.
  • End-to-end differentiable pipelines might combine classical forecasting with neural components more easily.
  • Automated retraining on growing datasets could become routine without custom parallel implementations.

Load-bearing premise

Casting forecasting operations as pure JAX functions will deliver meaningful gains in scalability, parallelism, and composability over existing Python libraries without introducing prohibitive usability costs or missing critical statistical features.

What would settle it

A direct benchmark on a large multi-series dataset where Chronax shows no execution speedup, requires more user code, or lacks standard forecasting methods compared with established Python libraries would falsify the expected advantages.

Figures

Figures reproduced from arXiv: 2604.16719 by Aileen Huang, Amy Greenwald, Anvesha Tiwary, Denizalp Goktas, Gerardo Riano, Lorraine Yang, Omkar Tekawade, Sunit Jadhav, Xan Carey, Yash Deshmukh.

Figure 1
Figure 1. Figure 1: Conformal validation assuming T = 14, K = 3, and h = 4. For w = 1, tw = 2; for w = 2, tw = 6; for w = 3, tw = 10. Circles (◦) denote training observations; Xs (×) denote the h calibration steps used for conformal scoring. Each successive calibration window’s training set grows by h observations. 2. Generate forecasts for each window. For each calibration window w, we fit the forecasting model fi on the tra… view at source ↗
Figure 2
Figure 2. Figure 2: Distribution of Chronax/Statsforecast performance ratios for three datasets and six metrics. Columns show [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Heatmap of Chronax/Statsforecast benchmarking ratios for the Airline Passengers dataset across six metrics. [PITH_FULL_IMAGE:figures/full_fig_p017_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Heatmap of Chronax/Statsforecast benchmarking ratios for the Daily Female Births dataset across six metrics. [PITH_FULL_IMAGE:figures/full_fig_p018_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Heatmap of Chronax/Statsforecast benchmarking ratios for the Room Temperature dataset across six metrics. [PITH_FULL_IMAGE:figures/full_fig_p019_5.png] view at source ↗
read the original abstract

Time-series forecasting is central to many scientific and industrial domains, such as energy systems, climate modeling, finance, and retail. While forecasting methods have evolved from classical statistical models to automated, and neural approaches, the surrounding software ecosystem remains anchored to the traditional Python numerical stack. Existing libraries rely on interpreter-driven execution and object-oriented abstractions, limiting composability, large-scale parallelism, and integration with modern differentiable and accelerator-oriented workflows. Meanwhile, today's forecasting increasingly involves large collections of heterogeneous time series data, irregular covariates, and frequent retraining, placing new demands on scalability and execution efficiency. JAX offers an alternative paradigm to traditional stateful numerical computation frameworks based on pure functions and program transformations such as just-in-time compilation and automatic vectorization, enabling end-to-end optimization across CPUs, GPUs, and TPUs. However, this modern paradigm has not yet been fully incorporated into the design of forecasting systems. We introduce Chronax, a JAX-native time-series forecasting library that rethinks forecasting abstractions around functional purity, composable transformations, and accelerator-ready execution. By representing preprocessing, modeling, and multi-horizon prediction as pure JAX functions, Chronax enables scalable multi-series forecasting, model-agnostic conformal uncertainty quantification, and seamless integration with modern machine learning and scientific computing pipelines.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The manuscript introduces Chronax, a JAX-native library for univariate statistical forecasting and conformal inference. It claims that representing preprocessing, modeling, and multi-horizon prediction as pure JAX functions enables scalable multi-series forecasting, model-agnostic conformal uncertainty quantification, and seamless integration with modern differentiable and accelerator-oriented ML pipelines, overcoming limitations of traditional Python libraries reliant on interpreter-driven and object-oriented designs.

Significance. If the library's design delivers the asserted gains in scalability, parallelism, and composability without prohibitive usability or statistical-feature costs, the work could meaningfully advance time-series forecasting by bridging classical statistical methods with JAX's program transformations (JIT, vmap, autodiff) and hardware accelerators. This would be particularly relevant for domains handling large heterogeneous series collections with frequent retraining. The absence of any empirical support, however, prevents a positive assessment of realized impact.

major comments (2)
  1. [Abstract] Abstract: The central claims that Chronax 'enables scalable multi-series forecasting' and 'accelerator-ready execution' with 'meaningful' advantages over existing libraries are unsupported; no runtime measurements, scaling curves, accuracy metrics, or head-to-head comparisons against statsmodels, sktime, or GluonTS are provided anywhere in the manuscript.
  2. [Introduction] Introduction (and library-design sections): The premise that casting forecasting operations as pure JAX functions will yield practical improvements in composability and parallelism without missing critical statistical capabilities or incurring prohibitive usability costs is asserted but never tested; the manuscript contains no ablation studies, usability evaluations, or demonstrations on realistic multi-series workloads.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive feedback on our manuscript. We appreciate the emphasis on the need for empirical evidence to support the claims regarding scalability and usability of Chronax. We will revise the manuscript to include the requested benchmarks and evaluations.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claims that Chronax 'enables scalable multi-series forecasting' and 'accelerator-ready execution' with 'meaningful' advantages over existing libraries are unsupported; no runtime measurements, scaling curves, accuracy metrics, or head-to-head comparisons against statsmodels, sktime, or GluonTS are provided anywhere in the manuscript.

    Authors: We fully agree that the manuscript would benefit from quantitative support for these claims. In the revised version, we will add comprehensive experiments including runtime benchmarks on various hardware (CPU, GPU, TPU), scaling experiments with increasing numbers of series, accuracy metrics for forecasting and conformal prediction, and direct comparisons with statsmodels, sktime, and GluonTS using standard time series datasets. This will provide concrete evidence of the advantages. revision: yes

  2. Referee: [Introduction] Introduction (and library-design sections): The premise that casting forecasting operations as pure JAX functions will yield practical improvements in composability and parallelism without missing critical statistical capabilities or incurring prohibitive usability costs is asserted but never tested; the manuscript contains no ablation studies, usability evaluations, or demonstrations on realistic multi-series workloads.

    Authors: This observation is correct, and we acknowledge the lack of empirical testing for the design premises. We will incorporate ablation studies to isolate the effects of JAX transformations on performance and composability, usability evaluations through API complexity analysis and example walkthroughs, and detailed case studies on realistic multi-series workloads (e.g., large-scale retail or energy forecasting). We will also verify and document that no critical statistical capabilities are lost compared to traditional libraries. revision: yes

Circularity Check

0 steps flagged

No circularity: library introduction paper with no derivation chain

full rationale

This is a software library announcement paper that introduces Chronax by describing its JAX-native design for functional purity and composability in forecasting tasks. The abstract and text contain no equations, no fitted parameters, no predictions of numerical results, and no self-citations used to justify uniqueness theorems or ansatzes. Claims about scalability and integration are presented as design motivations rather than derived outputs, so no load-bearing step reduces to its own inputs by construction. The derivation chain is absent, making the paper self-contained against external benchmarks with no circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The contribution is a software library; no mathematical free parameters, domain axioms, or new invented entities are introduced in the abstract.

pith-pipeline@v0.9.0 · 5563 in / 1097 out tokens · 45140 ms · 2026-05-10T08:12:12.809456+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

11 extracted references · 11 canonical work pages

  1. [1]

    URL https: //doi.org/10.1214/23-AOS2276

    doi: 10.1214/23-AOS2276. (Cited on page 4.) Jui-Sheng Chou and Duc-Son Tran. Forecasting energy consumption time series using machine learning techniques based on usage patterns of residential householders.Energy, 165:709–726,

    work page doi:10.1214/23-aos2276

  2. [2]

    Daily total female births in california, 1959,

    (Cited on page 1.) Doug Cresswell. Daily total female births in california, 1959,

    work page 1959

  3. [3]

    Accessed: 2026-01-08

    URL https://www.kaggle.com/datasets/ dougcresswell/daily-total-female-births-in-california-1959 . Accessed: 2026-01-08. (Cited on page 9.) Alexiei Dingli and Karl Sant Fournier. Financial time series forecasting-a machine learning approach.Machine Learning and Applications: An International Journal, 4(1/2):3,

    work page 1959

  4. [4]

    Statsforecast: Lightning fast forecasting with statistical and econo- metric models

    (Cited on page 1.) Azul Garza, Max Mergenthaler, Cristian Challu, and Kin Olivares. Statsforecast: Lightning fast forecasting with statistical and econo- metric models. PyCon Salt Lake City, Utah, US 2022,

    work page 2022

  5. [5]

    (Cited on page 2.) Md Sabbirul Haque, Md Shahedul Amin, and Jonayet Miah

    URL https://github.com/Nixtla/statsforecast. (Cited on page 2.) Md Sabbirul Haque, Md Shahedul Amin, and Jonayet Miah. Retail demand forecasting: a comparative study for multivariate time series.arXiv preprint arXiv:2308.11939,

    work page arXiv

  6. [6]

    Tsururu: A python-based time series forecasting strategies library.arXiv preprint arXiv:2509.15843,

    (Cited on page 1.) Alina Kostromina, Kseniia Kuvshinova, Aleksandr Yugay, Andrey Savchenko, and Dmitry Simakov. Tsururu: A python-based time series forecasting strategies library.arXiv preprint arXiv:2509.15843,

    work page arXiv

  7. [7]

    Accessed: 2026-01-08

    URL https://www.kaggle.com/datasets/ vitthalmadane/ts-temp-1. Accessed: 2026-01-08. (Cited on page 9.) Spyros Makridakis, Evangelos Spiliotis, Vassilios Assimakopoulos, Artemios-Anargyros Semenoglou, Gary Mulder, and Konstanti- nos Nikolopoulos. Statistical, machine learning and deep learning forecasting methods: Comparisons and ways forward.Journal of th...

    work page 2026

  8. [8]

    Accessed: 2026-01-05

    URL https://www.kaggle.com/datasets/brmil07/ air-passengers-dataset. Accessed: 2026-01-05. (Cited on page 9.) Pablo Montero-Manso and Rob J Hyndman. Principles and algorithms for forecasting groups of time series: Locality and globality. International Journal of Forecasting, 37(4):1632–1653,

    work page 2026

  9. [9]

    Olivares, Federico Garza, David Luo, Cristian Challu, Max Mergenthaler, and Artur Dubrawski

    (Cited on page 1.) Kin G Olivares, Azul Garza, David Luo, Cristian Challú, Max Mergenthaler, Souhaib Ben Taieb, Shanika L Wickramasuriya, and Artur Dubrawski. Hierarchicalforecast: A reference framework for hierarchical forecasting in python.arXiv preprint arXiv:2207.03517,

    work page arXiv

  10. [10]

    A systematic review of python packages for time series analysis.arXiv preprint arXiv:2104.07406,

    (Cited on page 3.) Julien Siebert, Janek Groß, and Christof Schroth. A systematic review of python packages for time series analysis.arXiv preprint arXiv:2104.07406,

    work page arXiv

  11. [11]

    (Cited on page 1.) 13 Simulacrum A Additional Experimental Results The detailed benchmark results tables in this appendix depict results for three datasets—Airline Passengers, Daily Female Births, and Room Temperature. We report model-wise performance across both Chronax and StatsForecast libraries, including latency metrics (cold start and warm start exe...

    work page 2007