Paper: arXiv 2512.08851

Authors: Daniel Egger, Jacob Vestal

Abstract

Hoeffding’s Inequality provides the maximum probability that a series of n draws from a bounded random variable differ from the variable’s true expectation u by more than given tolerance t. The random variable is typically the error rate of a classifier in machine learning applications. Here, a trading strategy is premised on the assumption of an underlying distribution of causal factors, in other words, a market regime, and the random variable is the performance of that trading strategy. A larger deviation of observed performance from the trader’s expectation u can be characterized as a lower probability that the financial regime supporting that strategy remains in force, and a higher probability of financial regime change. The changing Hoeffding probabilities can be used as an early warning indicator of this change.

Complexity vs Empirical Score

  • Math Complexity: 3.5/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Philosophers — conceptual discussion, limited math and data

Why this score: The paper presents a novel conceptual framework for applying Hoeffding’s Inequality as an early warning signal for financial regime change. However, it relies entirely on toy examples and basic conceptual math without providing any empirical backtests, historical market data validation, or algorithmic implementation details.

Research Flowchart

  flowchart TD
    A["Research Goal: Detect Financial Regime Change Early"] --> B["Input: Trading Strategy Performance & Expectations"]
    B --> C["Model Strategy Returns as Bounded Random Variable"]
    C --> D["Apply Hoeffding's Inequality to Calculate Deviation Probability"]
    D --> E["Monitor Changing Probabilities Over Time"]
    E --> F["Outcome: Early Warning Indicator for Multi-Asset Regime Shifts"]

Cited References (10)

  1. A new approach to the economic analysis of nonstationary time series and the business cycle (1989) — link
  2. Weighted sums of certain dependent random variables (1967) — link
  3. International asset allocation with regime shifts (2002) — link
  4. Proceedings of the 2024 SIAM International Conference on Data Mining ( SDM ) (2024) — link
  5. Regime switching in stock market returns (1997) — link
  6. The missing factor in Hoeffding ’s inequalities (1995) — link
  7. Concentration inequalities for statistical inference (2021) — link
  8. Kernel representation learning with dynamic regime discovery for time series forecasting (2024) — link
and 2 more
  1. Learning from data (2012) — link
  2. Probability inequalities for sums of bounded random variables (1963) — link

0 of 10 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.