The Simulacrum: Decision-Theoretic Pretraining for Near-Optimal Time-Series Forecasting and Inference

2026-06-26

AI Summary

This work proposes a decision-theoretic neural pretraining framework to address key challenges in time series analysis, including finite-sample bias, poor calibration, and forecast combination. By jointly modeling the data-generating process and decision objectives within a simulated environment, the method trains neural networks via hierarchical simulation to approximate optimal decision rules, enabling high-quality zero-shot inference without real-world data. The approach innovatively integrates decision theory with deep learning, allowing explicit control over risk, bias, minimax performance, and calibration consistency, thereby effectively solving problems that are analytically intractable or computationally prohibitive. Empirical results demonstrate substantial improvements over conventional methods such as maximum likelihood estimation and AICc in AR(p) modeling and forecast combination tasks, while achieving competitive or superior performance against state-of-the-art statistical and deep learning models on real-world benchmarks.

Abstract

We introduce a neural network-based framework for learning time series estimators through a process we term decision-theoretic pretraining. Analysts specify a generative world, a distribution over data-generating processes, and a target decision objective. A neural network trained on stratified simulations from this world approximates the corresponding optimal decision rule, yielding a neural estimator that provides forecasts, parameter estimates, predictive intervals, or model-selection for zero-shot inference on previously unseen time series. The joint specification of the generative world and objective enables the estimators to directly approximate process-level, finite-sample properties: near-optimal risk, bias control, minimax performance, and uniform calibration. Our experiments demonstrate that these neural estimators can outperform traditional baselines such as maximum likelihood estimation and model selection via AICc, for the same model structural model classes. Furthermore, even when trained purely on simulations of structural models, they achieve competitive or state-of-the-art forecasting accuracy on major real-world benchmarks, compared with statistical, neural or large pre-trained models. We illustrate the framework by addressing two longstanding challenges: finite-sample bias and miscalibration in AR(p) models, and the forecast combination puzzle. These applications highlight the approach's main advantage: its ability to approximate solutions to analytically intractable or computationally prohibitive time series problems, including complex structural equations or optimality criteria. Ultimately, by enabling explicit control over decision-theoretic trade-offs, the framework equips analysts with highly efficient estimation tools tailored to their specific analytical needs.

Problem

• time-series forecasting
• finite-sample bias
• forecast combination puzzle
• miscalibration
• decision-theoretic inference

Innovation

• decision-theoretic pretraining
• neural time series estimation
• zero-shot inference
• finite-sample optimality
• simulation-based learning