Nonlinear scale dynamics and distribution choice in Bitcoin VaR-ES forecasting
Published:
Mar 16, 2026
Volume:
24
Keywords:
Bitcoin
GAMLSS
Value-at-Risk
Expected Shortfall
Abstract
We forecast daily Bitcoin Value-at-Risk and Expected Shortfall using the Generalized Additive Models for Location, Scale, and Shape (GAMLSS) framework. 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.
How to cite
Lucas M. Oliveira, Luis G. Felix, Anny K. G. Rodrigues. Nonlinear scale dynamics and distribution choice in Bitcoin VaR-ES forecasting. Brazilian Review of Finance, v. 24, n. 1, 2026. p. e202604. DOI: 10.12660/rbfin.v24n1.2026.97569.
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