Overparametrized models with posterior drift

ArXiv ID: 2506.23619 “View on arXiv”

Authors: Guillaume Coqueret, Martial Laguerre

Abstract

This paper investigates the impact of posterior drift on out-of-sample forecasting accuracy in overparametrized machine learning models. We document the loss in performance when the loadings of the data generating process change between the training and testing samples. This matters crucially in settings in which regime changes are likely to occur, for instance, in financial markets. Applied to equity premium forecasting, our results underline the sensitivity of a market timing strategy to sub-periods and to the bandwidth parameters that control the complexity of the model. For the average investor, we find that focusing on holding periods of 15 years can generate very heterogeneous returns, especially for small bandwidths. Large bandwidths yield much more consistent outcomes, but are far less appealing from a risk-adjusted return standpoint. All in all, our findings tend to recommend cautiousness when resorting to large linear models for stock market predictions.

Keywords: Out-of-sample Forecasting, Posterior Drift, Equity Premium Prediction, Overparametrization, Model Complexity

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail
• Why: The paper features high math complexity with extensive theoretical derivations (e.g., Proposition 1, risk decompositions, large-dimensional asymptotics) and rigorous empirical analysis including Monte Carlo simulations, sub-period backtests, and sensitivity analysis on bandwidth parameters for equity premium forecasting.

  flowchart TD
    A["Research Goal<br>Assess impact of posterior drift<br>on overparametrized model forecasting"] --> B["Methodology<br>Estimate linear models with varying bandwidths<br>Analyze out-of-sample forecasting accuracy"]
    B --> C["Data Input<br>Equity premium historical data<br>Train vs. Test samples with regime shifts"]
    C --> D["Computational Process<br>Simulate varying holding periods<br>(e.g., 15 years) across sub-periods"]
    D --> E["Key Finding 1<br>Small bandwidths show<br>highly heterogeneous returns"]
    D --> F["Key Finding 2<br>Large bandwidths offer consistency<br>but poor risk-adjusted returns"]
    E & F --> G["Conclusion<br>Recommend cautiousness using large<br>linear models for stock market prediction"]