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Adaptive Window Selection for Financial Risk Forecasting

Yinhuan Li, Chenxin Lyu, Ruodu Wang

TL;DR

A data-driven online learning method that adaptively determines the window size in a sequential manner, called the bootstrap-based adaptive window selection (BAWS), that 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.

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.

Adaptive Window Selection for Financial Risk Forecasting

TL;DR

A data-driven online learning method that adaptively determines the window size in a sequential manner, called the bootstrap-based adaptive window selection (BAWS), that 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.

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.
Paper Structure (13 sections, 3 theorems, 57 equations, 12 figures, 4 tables, 1 algorithm)

This paper contains 13 sections, 3 theorems, 57 equations, 12 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Methodology
  3. Problem setup
  4. Bootstrap-based threshold specification
  5. Error control in window selection
  6. Window selection for VaR and ES forecasts
  7. Theoretical guarantee in a simple setting
  8. Simulation studies
  9. Scenario 1: Discrete structural changes
  10. Scenario 2: Continuous mean shifts
  11. Scenario 3: Dynamic volatility shifts
  12. Empirical analysis
  13. Conclusion

Key Result

Proposition 1

Under the global null $H_{0}^{t,k}:\ X_{t-k},\ldots,X_{t-1}\sim P_t$, the family-wise error rate satisfies

Figures (12)

  • Figure 1: The patterns of estimators over time under Setting A1.
  • Figure 2: The patterns of estimators over time under Setting A2.
  • Figure 3: The patterns of estimators over time under Setting A3.
  • Figure 4: The patterns of estimators over time under Setting B1.
  • Figure 5: The patterns of estimators over time under Setting B2.
  • ...and 7 more figures

Theorems & Definitions (9)

  • Proposition 1
  • proof
  • Remark 1
  • Theorem 1
  • proof
  • Remark 2
  • Corollary 1
  • proof
  • Example 1: Naive two-regime example: BAWS selects $250$ over $500$