Algometrics: Forecasting Under Algorithmic Feedback
The paper introduces 'algometrics', a framework for time series forecasting when predictive models influence the data they aim to predict. It distinguishes historical risk from deployment risk and proves three key results: deployment risk is not identifiable from passive historical data alone; historical model rankings can invert due to crowding; and randomized actions can identify short-horizon linear feedback with a finite-sample bound. The findings suggest that benchmarks in algorithmic markets should report feedback sensitivity alongside predictive accuracy.
Article intelligence
Key points
- Introduces algometrics framework for forecasting with algorithmic feedback.
- Proves deployment risk is not identifiable from passive historical data alone.
- Shows historical model rankings can invert under crowding.
- Derives finite-sample bound for deployment risk estimation via randomized actions.
Why it matters
This matters because introduces algometrics framework for forecasting with algorithmic feedback.
Technical impact
May affect model selection, inference cost, product capability, and evaluation benchmarks.
[2605.23978] Algometrics: Forecasting Under Algorithmic Feedback
[Submitted on 13 May 2026]
Title:Algometrics: Forecasting Under Algorithmic Feedback
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Abstract:In algorithmic markets, predictive models become part of the data-generating process they aim to forecast. Once their outputs are converted into trades, allocations, execution schedules, or risk controls, they change the future data on which they are evaluated. I introduce algometrics, a framework for time series whose evolution depends on the predictive algorithms forecasting them. The framework distinguishes historical risk, measured under passive forecasting, from deployment risk, measured when forecasts drive actions. I prove three results. First, deployment risk is not identifiable from passive historical data alone: even in a one-step linear feedback model, infinitely many algorithm-mediated environments induce the same historical law while implying different deployment risks for the same forecaster. Second, historical model rankings can invert under crowding, so a predictor with lower passive error can have higher deployment error once similar algorithms are adopted. Third, randomized or instrumented actions identify short-horizon linear feedback, and I derive a finite-sample bound for deployment-risk estimation. These results suggest that time-series benchmarks in algorithmic markets should report feedback sensitivity alongside predictive accuracy.
Subjects:
Machine Learning (cs.LG); Econometrics (econ.EM); Statistical Finance (q-fin.ST); Trading and Market Microstructure (q-fin.TR)
Cite as: arXiv:2605.23978 [cs.LG]
(or arXiv:2605.23978v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2605.23978
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Marc Schmitt [view email] [v1] Wed, 13 May 2026 20:05:54 UTC (64 KB)
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