Five basis points on ICP is the largest utility gain Local Linear Forests deliver over a plain random forest. Across eight coins, LLF produces between 3.85% and 3.98% of realized utility per unit wealth. RF delivers between 3.91% and 3.95%, while the paper's own perfect-forecast ceiling is 4.00%.
Noot and Sifat apply Local Linear Forests to daily realized volatility for eight coins. The estimator comes from Friedberg, Tibshirani, Athey and Wager. A random forest assigns a weight to every historical day according to how often it shares a leaf with today. LLF uses those weights as a kernel, then fits a ridge-penalized local linear regression at each test point. The forest selects historical days that resemble today; the local regression fits a slope through those neighbours rather than returning their average. The paper calls the plain forest's weakness "adaptive rigidity": the standard RF prediction "fails to capture local adaptivity in feature relationships", holding the same feature relationships across all market conditions.
The sample covers BTC, ETH, USDT, BNB, BCH, LTC, ICP and MATIC from 1 August 2021 to 1 June 2024, using daily data. Each coin has 1,056 return observations. The feature set contains roughly thirty market and technical series: five lags of realized variance, OHLC, high-minus-low, volume, five lags of returns, then RSI, MACD, Bollinger, Keltner, VWAP, Ichimoku and the rest. Optuna cross-validates the forest and LLF hyperparameters over 50 iterations. Out-of-sample performance comes from a single 70-30 train-test split. GARCH(1,1), GJR-GARCH, HAR-RV and a plain random forest provide the benchmarks.
The economic test uses the risk-targeting investor from Bollerslev, Hood, Huss and Pedersen. Position size equals (SR/gamma) divided by forecast variance. Gamma is 2, the assumed annualized Sharpe is 0.4 and the volatility target is 20%. Every model is measured against the 4.00% realized utility per unit wealth delivered by a perfect forecast.
Random forest is the live comparison
LLF records the lowest out-of-sample RMSE for eight of eight coins. For BTC, it scores 0.541 against RF 0.705, GARCH 1.324, GJR-GARCH 1.293 and HAR-RV 1.250. ETH comes in at 0.256 against RF 0.724. ICP is 0.705 against RF 1.856. The Model Confidence Set retains every model that cannot be statistically separated from the best. At alpha = 0.1 with block bootstrap length 7, LLF has an inclusion rate of 1.000 on RMSE. GARCH(1,1), GJR-GARCH and HAR-RV register 0.000 on every loss function.
The parameter estimates show how little the asymmetric benchmark contributes. For five of the eight coins, the GJR leverage term is negative: BCH -0.312, LTC -0.040, ICP -0.041, USDT -0.012 and MATIC -0.005. Only BTC, ETH and BNB have positive estimates. Across most of this sample, the asymmetric benchmark has no equity-style asymmetry to add. GARCH and GJR-GARCH RMSEs are within 0.06 on seven of the eight coins. BCH is the exception, at 2.859 against 3.103.
QLIKE makes random forest the relevant opponent and splits the sample four to four. LLF wins on ETH, 0.009 against 0.026; BCH, 0.020 against 0.037; ICP, 0.014 against 0.038; and LTC, 0.020 against 0.025. RF wins BTC at 0.031 against 0.061, USDT at 0.048 against 0.144, BNB at 0.028 against 0.030 and MATIC at 0.025 against 0.027. The authors report this themselves. They argue that RF produces more extreme errors, whereas LLF gives stronger point estimates under squared-error-sensitive losses. QLIKE punishes proportional variance error, precisely the error that matters when a position rule divides by the forecast. The abstract's "consistently outperform" claim and the results section's own concession therefore refer to different tables.
The cleanest ranking comes from the Model Confidence Set, and it supports keeping RF in the discussion. RF records inclusion rates of 0.375 on RMSE, 0.375 on MAE, 0.500 on QLIKE and 0.500 on negative utility. LLF posts 1.000, 0.875, 0.875 and 0.875. The authors summarize the result this way: "While RF remains competitive, it is noticeably outperformed by LLF overall." These rates represent shares of the eight coins. RF remains in the confidence set for three coins on RMSE and four on QLIKE and utility. A model that survives half the time under the loss function driving position size can stay in production.
Does the utility gain cover the switch?
LLF realizes between 3.85% and 3.98% against the 4.00% ceiling. RF realizes between 3.91% and 3.95%. RF leads on BTC, 3.94% against 3.85%; USDT, 3.91% against 3.77%; and BNB, 3.95% against 3.94%. Both models reach 3.95% on MATIC. The tally is four coins to three with one tie. LLF's largest advantage is five basis points on ICP, 3.97% against 3.92%. The paper concedes as much in one line: "Again, only RF provides comparable utility." GARCH ranges from 3.46% to 3.81%, while HAR-RV spans 3.09% to 3.81%. Even models excluded from every confidence set capture most of the available utility.
Turnover carries no charge in this exercise. Because allocation is inversely proportional to the forecast, a jumpier forecast trades more on our reading. The utility metric misses that cost.
A forecast improvement worth five basis points of gross utility on its best coin, measured against the model already running, does not justify replacement.
Three years, one bear market
Out-of-sample evidence rests on one 70-30 split from a 1,056-day window. The paper does not specify whether hyperparameter tuning used only the training portion. It says merely that tuning was "performed and cross-validated with the Optuna package with 50 iterations". In-sample fits are extreme. ICP produces an LLF RMSE of 0.106 against GARCH's 4.166. The authors acknowledge the risk: "LLF's strong performance in-sample may result from overfitting, where the model fits the noise in the data rather than the underlying patterns," and treat the out-of-sample table as the answer. Fair, within the limits of one split.
Regime results offer more evidence than the split alone suggests. BTC days are classified using a 30-day rolling window rule: above +5% is bull, below -5% is bear, and the remainder is consolidating. LLF's mean squared forecast error is 0.268 in bear periods, 0.194 in consolidating periods and 0.447 in bull periods. GARCH records 2.235, 1.532 and 1.964. Across the seven non-Tether coins, LLF enters the confidence set at a rate of 1.000 in all three phases. RF records 0.571, 0.429 and 0.571. The main text establishes a real gap on one asset, the appendix adds six more coins, and all observations remain inside one cycle. The introduction and discussion claim a 40% to 60% error reduction during transition periods. We did not find that claim linked to a specific table or test.
The simulations identify the source of the effect. With d = 0, n = 1000 and sigma = 1, LLF has RMSE 0.130 against RF's 0.045. The paper states that in low-noise, low-dimensional settings LLF "underperforms, often exhibiting the highest error." More noise reverses the order. At d = 0, sigma = 10 and n = 5000, LLF scores 0.317 against RF 0.429 and XGBoost 0.815. Holding the same noise and sample size, LLF reaches 0.526 for d = 5 and 0.327 for d = 10. Its advantage depends on the noise regime. The out-of-sample table has to establish whether daily crypto data occupy that regime. It does so on RMSE: LLF beats RF across all eight coins, with gaps of 0.468 on ETH and 1.151 on ICP.
The whole mid-cap row
The cross-sectional section presents mid-cap coins as more predictable. Its root mean squared log error is scale-free, allowing comparison across coins with different volatility. Under LLF, mid-cap RMSLE is 0.207 against 0.382 for large caps. Squared-log-error standard deviation is 0.072 against 0.498. Every one of the five models has the same direction: RF 0.254 against 0.267, GARCH 0.503 against 0.663, GJR-GARCH 0.506 against 0.663 and HAR-RV 0.460 against 0.620. LLF stands apart in the size of the difference, at 46%, compared with 5% for RF and 24%, 24% and 26% for GARCH, GJR-GARCH and HAR-RV. RF also forecasts large caps better than LLF, 0.267 against 0.382. We did not find the introduction's 30% figure attached to a table. Mid-cap means a market capitalization of 5 to 10 billion USD. With eight coins in total, including ICP and MATIC, the cross-section is thin.
Feature importance weakens the modelling case. Among thirty-plus indicators, the main inputs are high-minus-low, volume in euros, lagged returns, lagged RV and a moving average of RV. When five lags of RV and a range supply the useful information, smoothing carries the case for a two-stage adaptive-kernel estimator over a forest. Its value is the value shown in the utility table.
We could not test any of this ourselves. We hold no cryptocurrency prices, leaving the eight daily OHLC and volume series unavailable. Substituting equities would test a different model under a different noise regime. We also did not find a statement giving the intraday sampling frequency or the venue used to construct the RV target.
There is one point of continuity. In our review of a NEPSE volatility study, the model ranking flipped with the loss function, while a structural break mattered more than the specification. The same pattern appears here, and the authors do the honest thing by publishing the table that reveals it.