A Comparison of Regression Models for Cryptocurrency Forecasting Across 14 Assets and Three Liquidity Tiers

We compare classical and modern regression models for next-day cryptocurrency forecasting on 14 USD-denominated coins across three liquidity tiers from 2018 through 2025, and we use the resulting panel to formally test three pre-specified hypotheses. The features are a strictly past-only 28-element set; the evaluation uses expanding-window walk-forward cross-validation with nested hyperparameter tuning, stationary block-bootstrap 95% confidence intervals, and pairwise Diebold–Mariano tests. Methodologically, we derive a bias-variance bound that turns the ‘no model beats the mean’ observation from a null finding into a predicted outcome under weak-form market efficiency. Empirically, (H1) the threshold–effect interaction is not supported (slope −1.7 × 10−4, 95% CI [−4.8 × 10−4, +1.4 × 10−4], p = 0.25). (H2) Statistical loss minimisation is decoupled from risk-adjusted economic outcome: the cluster-bootstrapped 95% CI for the Spearman rank correlation between the within-ticker MAE rank and within-ticker post-cost Sharpe rank is [−0.39, +0.10] overall, lies *strictly below zero* on the mid-cap (CI [−0.71, −0.04]) and long-tail (CI [−0.26, −0.09]) tiers, and decisively rejects perfect alignment (ρ = +1) on every tier. None of the seven (ticker, model) pairs with annualised Sharpe ≥ 0.5 has a hit rate significantly different from 0.5; high-Sharpe outcomes reflect return skew, not directional skill—formally predicted by a closed-form Sharpe–MSE decoupling proposition we derive in Section 3.6 under non-zero return skewness. (H3) Lo–MacKinlay variance ratio tests show top-tier coins are indistinguishable from a random walk (|z| ≤ 1.5 at q ∈ {2, 5, 10}), while mid- and long-tail tiers reject the random-walk null at q = 2 (z = −2.36, z = −2.60). The findings extend across two robustness layers. An AR(1)-GARCH(1,1) baseline produces R2 ≈ −0.005 on every tier and is indistinguishable from Lasso, supporting the bias-variance bound; Giacomini–White conditional predictive ability tests reject equal predictive ability between Lasso and tree-based models on every coin in every tier, complicating naive DM interpretations; and a forward-walking 2026-Q1 holdout—83 daily observations per coin entirely outside the training window—confirms that H1 is even more decisively null on unseen data and that the H3 efficiency conclusion holds. Together, these results give a formally tested EMH-style picture for daily crypto: no model meaningfully forecasts log-returns; statistical accuracy and trading P&L are decoupled by an analytically derived mechanism; and weak-form efficiency is approximately satisfied in most liquid coins and in the convergence across the cross-section.