Nonlinear scale dynamics and distribution choice in Bitcoin VaR-ES forecasting
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Abstract
We forecast daily Bitcoin Value-at-Risk and Expected Shortfall using Generalized Additive Models for Location, Scale, and Shape (GAMLSS). A data-driven selection procedure chooses a Power Exponential distribution whose scale depends nonlinearly on lagged returns via a penalized spline. Macroeconomic, on-chain, and sentiment predictors are discarded. Out of sample, this specification achieves the lowest joint Fissler–Ziegel loss among four competing models, though Diebold–Mariano tests cannot reject equal predictive accuracy against a GARCH(1,1) benchmark. The evidence suggests that the functional form of the scale equation matters more than predictor breadth. A decomposition analysis shows that, once nonlinear scale dynamics are modeled, the Normal distribution achieves the lowest FZ0 across all predictor sets, outperforming every heavy-tailed alternative.
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References
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