Simulacrum: Decision‑Theoretic Pretraining for Near‑Optimal Time‑Series Forecasting and Inference
Abstract
We propose a neural network-based framework for time series forecasting and parameter estimation
that approximates optimal performance for a wide range of models and optimality criteria.
Trained on large-scale simulations of structural models with known ground truth,
the networks learn to map input time series to their corresponding forecasts and population parameters.
Once trained, they act as (neural) statistical estimators, producing forecasts and parameter
estimates for unseen data.
The training process can be adapted to target statistical decision-theory optimality
properties such as minimum forecast error,
unbiasedness, uniform calibration, model selection accuracy, and robustness.
These neural estimators outperform traditional methods
(e.g., Maximum Likelihood, selection by AIC) and achieve state-of-the-art accuracy on
major real dataset benchmarks, surpassing even complex AI models.
We demonstrate the framework by addressing two longstanding challenges:
the unbiased estimation of the AR(p) model class, and the forecast model combination puzzle.
The main advantage of the approach is its ability to approximate solutions to
analytically intractable or computationally prohibitive time series problems,
such as complex structural equations or optimality criteria.
Combined with inductive biases that can be expressed via neural architectures,
the framework offers a powerful tool for modernizing time series analysis and accelerating scientific research.
that approximates optimal performance for a wide range of models and optimality criteria.
Trained on large-scale simulations of structural models with known ground truth,
the networks learn to map input time series to their corresponding forecasts and population parameters.
Once trained, they act as (neural) statistical estimators, producing forecasts and parameter
estimates for unseen data.
The training process can be adapted to target statistical decision-theory optimality
properties such as minimum forecast error,
unbiasedness, uniform calibration, model selection accuracy, and robustness.
These neural estimators outperform traditional methods
(e.g., Maximum Likelihood, selection by AIC) and achieve state-of-the-art accuracy on
major real dataset benchmarks, surpassing even complex AI models.
We demonstrate the framework by addressing two longstanding challenges:
the unbiased estimation of the AR(p) model class, and the forecast model combination puzzle.
The main advantage of the approach is its ability to approximate solutions to
analytically intractable or computationally prohibitive time series problems,
such as complex structural equations or optimality criteria.
Combined with inductive biases that can be expressed via neural architectures,
the framework offers a powerful tool for modernizing time series analysis and accelerating scientific research.
