Algometrics: Forecasting Under Algorithmic Feedback
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910249812754432 |
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| author | Schmitt, Marc |
| author_facet | Schmitt, Marc |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_23978 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Algometrics: Forecasting Under Algorithmic Feedback Schmitt, Marc Machine Learning Econometrics Statistical Finance Trading and Market Microstructure 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. |
| title | Algometrics: Forecasting Under Algorithmic Feedback |
| topic | Machine Learning Econometrics Statistical Finance Trading and Market Microstructure |
| url | https://arxiv.org/abs/2605.23978 |