Paper: arXiv 2603.01157

Authors: Yinhuan Li, Chenxin Lyu, Ruodu Wang

Abstract

Risk forecasts in financial regulation and internal management are calculated through historical data. The unknown structural changes of financial data poses a substantial challenge in selecting an appropriate look-back window for risk modeling and forecasting. We develop a data-driven online learning method, called the bootstrap-based adaptive window selection (BAWS), that adaptively determines the window size in a sequential manner. A central component of BAWS is to compare the realized scores against a data-dependent threshold, which is evaluate based on an idea of bootstrap. The proposed method is applicable to the forecast of risk measures that are elicitable individually or jointly, such as the Value-at-Risk (VaR) and the pair of the VaR and the corresponding Expected Shortfall. Through simulation studies and empirical analyses, we demonstrate that BAWS generally outperforms the standard rolling window approach and the recently developed method of stability-based adaptive window selection, especially when there are structural changes in the data-generating process.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 8.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces an innovative bootstrap-based adaptive window selection (BAWS) framework that elegantly combines statistical theoretical properties (elicitability) with practical financial risk management. Its empirical evaluation across multiple simulated non-stationary regimes and real S&P 500 historical data offers rigorous validation, demonstrating clear superiority over fixed rolling windows.

Research Flowchart

  flowchart TD
    A[Research Goal: Adaptively select look-back window size for financial risk forecasting under structural changes] --> B[Data/Inputs: Historical financial data for elicitable risk measures like VaR and Expected Shortfall]
    B --> C[Methodology: Bootstrap-based Adaptive Window Selection - BAWS]
    C --> D[Computational Process: Sequentially compare realized forecast scores against a data-dependent bootstrap threshold]
    D --> E[Evaluation: Perform simulation studies and empirical cross-asset analysis vs. standard rolling & stability-based windows]
    E --> F[Key Outcomes: BAWS outperforms existing methods, especially during structural changes in data-generating processes]

Cited References (47)

  1. Comparing predictive accuracy (1995)
  2. Asymptotic statistics (2000)
  3. Weak convergence and empirical processes: with applications to statistics (2013)
  4. An academic response to Basel 3.5 (2014)
  5. Quantitative risk management: concepts, techniques and tools-revised edition (2015)
  6. Asymmetric least squares estimation and testing (1987)
  7. Expected Shortfall is jointly elicitable with Value at Risk-Implications for backtesting (2015) — link
  8. Higher order elicitability and Osband’s principle (2016)
and 39 more
  1. Backtesting expected shortfall (2014)
  2. On elicitable risk measures (2015)
  3. Risk measures with the CxLS property (2016)
  4. On the measurement of economic tail risk (2016)
  5. Elicitable distortion risk measures: A concise proof (2015)
  6. Making and evaluating point forecasts (2011)
  7. Coherence and elicitability (2016)
  8. A stability Principle for Learning Under Nonstationarity (2025)
  9. Elicitability and identifiability of tail risk measures — → 2404.14136
  10. A theory for measures of tail risk (2021)
  11. Forecasting in the presence of instabilities: How we know whether models predict well and how to improve them (2021)
  12. Selection of estimation window in the presence of breaks (2007)
  13. Optimal forecasts in the presence of structural breaks (2013)
  14. Rolling window selection for out-of-sample forecasting with time-varying parameters (2017)
  15. Forecasting stock returns (2013)
  16. Forecasting realized volatility: The choice of window size (2025)
  17. Improving forecast accuracy by combining recursive and rolling forecasts (2009)
  18. Adaptive forecasting in the presence of recent and ongoing structural change (2013)
  19. Forecasting stock returns: A time-dependent weighted least squares approach (2021)
  20. E-backtesting (2025) — link
  21. Monitoring value-at-risk and expected shortfall forecasts (2023)
  22. On Bayesian modeling of fat tails and skewness (1998)
  23. The jackknife and the bootstrap for general stationary observations (1989)
  24. Optimal versus naive diversification: How inefficient is the 1/N portfolio strategy? (2009)
  25. Systemic risk-driven portfolio selection (2022)
  26. Out-of-sample forecast tests robust to the choice of window size (2012)
  27. Market shocks and professionals’ investment behavior–Evidence from the COVID-19 crash (2021)
  28. Model Assessment and Selection under Temporal Distribution Shift (2024)
  29. A note on quantiles in large samples (1966)
  30. Some asymptotic theory for the bootstrap (1981)
  31. An MCMC approach to classical estimation (2003)
  32. A joint quantile and expected shortfall regression framework (2019)
  33. Limiting distributions for $L_1$ regression estimators under general conditions (1998)
  34. Dynamic semiparametric models for expected shortfall (and value-at-risk) (2019)
  35. Asymptotics for least absolute deviation regression estimators (1991)
  36. Weak Convergence and Empirical Processes: With Applications to Statistics (1996)
  37. The blockwise bootstrap for general empirical processes of stationary sequences (1995)
  38. Mixing and moment properties of various GARCH and stochastic volatility models (2002)
  39. Mixing: Properties and Examples (1994)

1 of 47 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.