2402.07532
Forecasting with Pairwise Gaussian Markov Models
Marc Escudier, Ikram Abdelkefi, Clément Fernandes, Wojciech Pieczynski
correctmedium confidence
- Category
- Not specified
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper’s theoretical comparison uses the L2-projection/Pythagoras argument to show PMM forecasting MSE is minimal under PMM data and derives the same linear-Gaussian k-step predictor and covariance recursion via the Markov form. The candidate solution reproduces these very steps and formulas. Aside from a small imprecision about identifying L2(σ(Y1:n)) with the linear span of Y’s (unneeded for the projection argument), the model matches the paper.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The theoretical core is correct and clearly demonstrates when and why PMM can outperform HMM for forecasting in linear-Gaussian settings. The empirical illustrations are useful. The work is incremental rather than groundbreaking, but it fills a gap and may encourage broader adoption of PMMs in forecasting. Minor notational/typographical issues and a few clarifications will further improve readability.