Noise Titration: Exact Distributional Benchmarking for Probabilistic Time Series Forecasting

Authors: Qilin Wang Date: 2026-03-23 Paper ID: openalex:2603.22219

Summary

This paper proposes a fundamental shift in probabilistic time series forecasting evaluation from passive sequence matching to interventionist, exact-statistical benchmarking using “Noise Titration.” This method involves injecting calibrated Gaussian noise into known dynamical systems, turning forecasting into an exact distributional inference task solvable via explicit negative log-likelihoods. To facilitate this, the authors extend the Fern architecture into a probabilistic model that efficiently parameterizes the Symmetric Positive Definite (SPD) cone for accurate covariance output. Evaluations reveal that large sequence-matching models fail under noise and non-stationarity, whereas the proposed Fern architecture successfully maintains structural fidelity and calibration by capturing the system’s invariant measure.

Key Contributions

• Introduced “Noise Titration,” a novel, interventionist benchmarking paradigm for probabilistic time series forecasting that uses mathematically explicit noise injection to convert evaluation into an exact distributional inference task.
• Developed an extension to the Fern architecture that natively parameterizes the Symmetric Positive Definite (SPD) cone to output calibrated joint covariance structures efficiently.
• Demonstrated that current state-of-the-art zero-shot foundation models fail systematically under non-stationary regime shifts and noise when evaluated using exact distributional tests.
• Showcased that the proposed Fern model maintains structural fidelity and statistical calibration by explicitly capturing the invariant measure and multivariate geometry of the underlying dynamics.

Limitations

The framework relies on the availability and fidelity of known chaotic or stochastic dynamical systems for noise titration, which may limit direct applicability to purely empirical, unknown real-world processes.

Open Questions & Future Work

• extending-noise-titration-beyond-gaussian

Key Concepts

• Noise Titration Benchmarking: A rigorous, interventionist benchmarking methodology for probabilistic time series forecasting that introduces calibrated Gaussian noise into known dynamical systems to create an exact distributional inference task.
• Fern Architecture Extension: An extension of the Fern architecture to a probabilistic generative model capable of natively parameterizing the Symmetric Positive Definite (SPD) cone for outputting calibrated joint covariance structures.

Limitations

The framework relies on the availability and fidelity of known chaotic or stochastic dynamical systems for noise titration, which may limit direct applicability to purely empirical, unknown real-world processes.

Links

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