Robust Real-Time Macroeconomic Trend Extraction: A Gradient Boosting Approach

Kinel, Michal (2026): Robust Real-Time Macroeconomic Trend Extraction: A Gradient Boosting Approach.

Abstract

Real-time macroeconomic trend extraction is chronically compromised by the end-point problem, a structural vulnerability that violently escalates during extreme exogenous shocks such as the Great Recession and the COVID-19 pandemic. Traditional filters anchored in $L_2$ loss minimization mechanically deform the long-run structural trend to absorb these massive, transitory outliers. To resolve this instability, we introduce the MacroBoost Hybrid (MBH) filter, a novel framework integrating penalized B-splines within a component-wise gradient boosting architecture optimized via an adaptive Huber quasi-likelihood. Through a rigorous quasi-real-time simulation, we demonstrate that ex-ante spectral alignment allows the MBH filter to perfectly match the baseline cyclical volatility of the industry-standard Hodrick-Prescott filter, achieving statistical parity in mean absolute error and exhibiting strictly zero mean bias under normal conditions. Crucially, during black swan events, the MBH filter categorically preserves the long-run trend by isolating the exogenous shock entirely within the cyclical component. This defense mechanism generates heavy tails in the revision distribution, structurally inflating the root mean square error and driving the Noise-to-Signal Ratio to exceed unity—a mathematical penalty we formally conceptualize as the "robustness tax" exacted for ensuring absolute trend integrity.

• Item Type: MPRA Paper
• Language: English
• Keywords: Real-time estimation, Hodrick-Prescott filter, Gradient Boosting, P-splines, Robust filtering, Business cycles
• Subjects: C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C53 - Forecasting and Prediction Methods ; Simulation Methods; E - Macroeconomics and Monetary Economics > E3 - Prices, Business Fluctuations, and Cycles > E32 - Business Fluctuations ; Cycles

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