CryptoL: Towards Scale Dominance and Physics Constraints Mitigation in Financial Multivariate Time Series Forecasting

Summary

The paper presents CryptoL, a framework for multivariate cryptocurrency OHLC forecasting targeting three problems: extreme cross-asset scale heterogeneity, normalization choices that destroy candlestick ordering, and physically invalid predictions. Its core is Two-Phase RevIN (TP-RevIN), which evaluates the training MSE in context-normalized coordinates rather than after inverse normalization; the authors formalize how original-space RevIN multiplies each sample's squared loss by s_n², effectively reweighting optimization toward large-scale assets (Proposition 1; effective asset distribution q_a ∝ π_a·s_a² in Eqs. 29–31). They further prove channel-dependent (CD) normalization preserves OHLC ordering while channel-independent (CI) need not (Theorem B.1, Proposition B.3), introduce a dynamic epsilon ε=10⁻⁵(μ²+10⁻¹²) that is approximately scale-equivariant, and add a hinge-style physics loss on OHLC inequality violations. Experiments use ~15.5M Binance OHLC rows across 16 assets and 7 timeframes with three decoder-only backbones (Timer, Timer-XL, Time-MoE). TP-RevIN generally improves MSE/MAE over standard RevIN; dynamic epsilon collapses SHIB's MAPE from 17362.6 to ~1.87–3.51 (Table 3); the physics loss drives violation rates near zero while keeping MAE competitive against an invertible-transformation baseline (Table 4). Main limitations: single runs with one training epoch, no variance estimates or significance tests, unexplained MAPE anomalies (e.g., 1.63e+4 in Table 2), missing cells in Table 10, and no released code.