Statistical Inference for Score Decompositions

Battle Count: 50

Highly relevant for quantitative trading and risk management. The paper directly addresses VaR backtesting under Basel regulation, volatility forecast evaluation, and the critical distinction between calibration and discrimination in risk models. The finding that well-calibrated forecasts (e.g., Historical Simulation) can have poor discrimination exposes shortcomings in current banking regulation that directly impact trading risk management. The decomposition framework enables traders and risk managers to diagnose whether forecast differences stem from calibration issues or information content differences. The connection to Mincer-Zarnowitz regression and traditional backtests makes it immediately applicable to existing risk management workflows. The inflation forecast application is relevant for macro-driven trading strategies.

Moderate complexity. The core estimation (linear recalibration via M-estimation) is straightforward and implemented in the provided R package 'SDI'. However, understanding and correctly applying the inference framework requires knowledge of: (1) asymptotic theory for misspecified regressions, (2) HAC covariance estimation, (3) the hybrid IU/UI testing principle for boundary cases, (4) generalized chi-squared distribution computation (Imhof's method), and (5) the distinction between smooth and non-smooth scoring functions. The R package abstracts much of this complexity. For practitioners, the main challenge is correctly specifying the recalibration information set W_it and interpreting the decomposition components in context.

The authors provide full replication material at https://github.com/marius-cp/SDI_replications and an R package 'SDI' at https://github.com/marius-cp/SDI. All data sources are publicly available (Philadelphia Fed for SPF and CPI data, Michigan Survey data site, Refinitiv for E-mini futures). Simulation code and parameters are fully specified. HAC covariance estimation follows standard procedures (Andrews 1991, Galvao and Yoon 2024). The paper includes detailed proofs in supplementary material.