Paper: arXiv 2611.04223

Authors: Ruihang Han, Li-Hsiang Lin

Abstract

Sequential forecast intervals are often evaluated by aggregate coverage even when calibration memory is bounded. This can be misleading when economically important states recur after long absences: a recent-only buffer may satisfy its overall coverage target while no longer containing errors from earlier episodes of the returning state. We study this problem in next-day financial range forecasting, holding the forecasting model, conformity score, adaptive update, and memory budget constant while varying the historical residual information available at each query. Recent-only first-in, first-out (FIFO) calibration is near nominal in aggregate but undercovers substantially during high-volatility states in both an exchange-traded fund development panel and a fixed stock panel. An unbounded state-history reference yields a lower observed stress-period interval score; Rare replay yields lower high-VIX interval scores than the matched Recent-n and Hybrid-n controls in both panels, and the state-structured versus recent-only contrast is largest near stress re-entry. Bounded calibration memory is therefore part of the forecasting information design, and aggregate calibration alone can conceal state-specific reliability failures.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a novel and empirically rigorous investigation into the limitations of aggregate calibration under bounded memory, particularly during recurrent financial stress. It employs a controlled experimental design with detailed statistical methodology and clear findings, making a significant contribution to uncertainty quantification in finance. The mathematical underpinnings of conformal prediction and HAR models are well-integrated with the empirical analysis.

Research Flowchart

  flowchart TD
    A[Research Goal: Evaluate Bounded-Memory Forecast Interval Calibration under Recurrent Financial Stress] --> B{Methodology: Compare Interval Coverage Across Memory Strategies};
    B --> C[Data/Inputs: Next-day Financial Range Forecasting (ETF/Fixed Stock Panels)];
    C --> D{Computational Process: Fixed Forecasting Model + Adaptive Update with Varying Historical Residual Information};
    D --> E[Memory Strategies: Recent-only FIFO, Unbounded State-History, Rare Replay, Hybrid];
    E --> F[Key Finding 1: Aggregate Coverage Can Mask State-Specific Undercoverage (High-Volatility States)];
    F --> G[Key Finding 2: State-History & Rare Replay Improve Coverage During Stress Re-entry vs. Recent-only];
    G --> H[Outcome: Bounded Calibration Memory is Part of Information Design; Aggregate Calibration Insufficient for Reliability];