Decomposing Rank Reversals under Temporal Nonstationarity: Alignment, Aggressiveness, and Instability

Paper: arXiv 2611.04116

Authors: Deying Song, Xueying Ding

Abstract

Under temporal nonstationarity, model performance rankings reverse across training horizons due to heterogeneous sensitivities to memory. While existing literature addresses adaptive lookbacks, effective model complexity, and empirical forecast evaluation in isolation, no unified framework explains the structural mechanics driving these rank reversals. We bridge this gap by deriving a model-agnostic decomposition of out-of-sample $R^2$ into target alignment, miscalibrated aggressiveness, and predictive instability. Within this framework, we mathematically characterize complexity phase boundaries, establish closed-form optimal-memory equations for ridge regression under local drift, and extend these guarantees to complex model architectures via surrogate bounds. We validate these theoretical dynamics by benchmarking 14 linear, tree-based, and neural architectures across large-scale financial panels. In doing so, our framework demonstrates that empirical model rank reversals are driven by predictable surges in miscalibrated aggressiveness, providing a rigorous mechanistic diagnosis of generalization under temporal shift.

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a highly mathematical framework for decomposing R^2 and analyzing rank reversals under nonstationarity. It rigorously validates its theoretical dynamics through extensive benchmarking across diverse financial panels, demonstrating strong empirical rigor. The unified framework and mechanistic diagnosis of generalization under temporal shift are highly novel.

Research Flowchart

  flowchart TD
    A[Research Goal: Explain Model Rank Reversals under Temporal Nonstationarity] --> B[Methodology: Derive Model-Agnostic R^2 Decomposition]
    B --> C{Decomposition Components:<br/>Alignment, Aggressiveness, Instability}
    C --> D[Computational Processes: Characterize Complexity Phase Boundaries & Optimal Memory]
    D --> E[Data/Inputs: 14 Linear, Tree, Neural Architectures on Large Financial Panels]
    E --> F[Validation: Benchmark Architectures & Observe Empirical Rank Reversals]
    F --> G[Key Finding: Rank Reversals Driven by Surges in Miscalibrated Aggressiveness]