Rigorous nonlinear system analysis

Background: The analysis rigorously compares three predictor classes (single-step, multi-step, intermediate) for prediction error in linear dynamical systems under both well-specified and misspecified scenarios. Nonlinear systems were only explored empirically.

Question / Future Work: A rigorous theoretical characterization and quantitative comparison of the prediction error for the three predictor classes (single-step, multi-step, intermediate) needs to be extended from the current stylized linear system setting to general nonlinear dynamical systems.

Why It Matters: Extending the rigorous statistical efficiency guarantees to nonlinear systems would validate the general applicability of the findings beyond linear time-invariant models, which is a significant limitation of the current theoretical work.

Evidence: These experiments suggest that the qualitative behavior predicted by our linear analysis may extend to some nonlinear systems. A rigorous treatment of this setting is left for future work.