Learned weights win all 54 QLIKE comparisons, with sizing still untested

Chan and Chan win 54 of 54 QLIKE comparisons on six cryptocurrencies, but a trader should budget for the smaller RMSE gains. Their neural network has a narrow job inside realized-volatility measurement, using hidden layers of [8,4] or [16,8] to replace equal weights. The forecast-loss result is clear. Whether it improves a volatility-targeted book remains future work in the paper.

Learn the weights, leave the five-minute terms alone

Each UTC day contains 288 five-minute bars. For realized variance, the squared open-to-close return of each bar enters a sum with weight one. Bipower variation uses products of adjacent absolute returns; Garman-Klass uses a high-low range term corrected by the squared return. The authors call these bar-level terms primitives. Summing them with equal weights gives the raw realized measure, or RRM.

Neural Realized Measures (NRM) leave the primitives unchanged and learn a weight for each. A softmax converts scores into positive weights, then scales them by 288 so their average is exactly one. Weights of one recover the RRM. A small MLP with hidden layers of [8,4] or [16,8] produces the scores from eight features per bar.

Three features describe candlestick shape: the body and both wicks divided by the range. Two express clock time through sine and cosine. One compares the bar with a same-day window of 12 to 144 bars through a log contrast. The remaining two describe the day, using the log median and log standard deviation of its primitives. A KL penalty draws the weights toward uniform, with its strength selected from 3e-4 to 3e-2.

Training fits the weights and forecasting head together under QLIKE. The heads are a single-lag regression (SF), HAR and MIDAS. Each asset, primitive and head gets a separate fit, leaving each coin with nine distinct NRM series. The authors explicitly describe the result as head-specific rather than a reusable measure.

The sample consists of five-minute OHLC bars from Binance spot price indices for BNB, BTC, DOGE, ETH, SOL and XRP. It spans 2020 to May 31, 2026. Validation covers June 2023 to May 2024; testing covers June 2024 to May 2026. Next-day log realized variance is the target.

Across six assets, three primitives and three heads, NRM wins all 54 paired QLIKE comparisons. Mean gains reach 7.23% for SF, 8.15% for HAR and 9.22% for MIDAS. The corresponding pooled Diebold-Mariano statistics are 4.06, 3.08 and 3.20. Following validation selection, NRM's mean test QLIKE is 0.374. RRM records 0.397, XGBoost 0.426, DeepVol 0.439 and HARNet 0.442.

What reaches position sizing from the 54-for-54 QLIKE record?

Less than the headline implies. SF improves RMSE by 3.35%, HAR by 1.30% and MIDAS by 1.54%. Each head still produces significant gains, with 17 of 18 wins apiece. Pooled DM statistics are 1.81 (p=0.035), 2.70 (p=0.003) and 2.83 (p=0.002). MAE improvements are 5.13%, 1.39% and 1.37%; the MIDAS MAE test falls short of 5% at p=0.062.

The authors deserve credit for selecting specifications on validation MSE. This avoids using QLIKE for both fitting and selection. Even with that separation, the training loss delivers gains about twice as large under SF and about six times as large under HAR and MIDAS.

Their conclusion acknowledges the pattern, describing the improvements as particularly consistent under QLIKE. They favor QLIKE because it permits forecast comparisons when a noisy proxy stands in for latent variance. Their target is such a proxy.

The objection remains. QLIKE measures ratio errors: a forecast 30% off on a quiet day incurs the same cost as a 30% miss on a crash day. Large days dominate RMSE on the variance scale. Those are also the days when a volatility targeter's sizing mistakes hurt most. HAR's mean RMSE improvement is 1.30%. I would budget for that RMSE figure and regard the QLIKE gain as an upper bound on what reaches the book.

Six correlated coins, two years

For each date, the pooled test averages RRM-minus-NRM loss differentials across asset-primitive pairs. Reported p-values are one-sided and unadjusted. With six coins moving together, that average offers less diversification than the count of 18 pairs suggests.

Results vary widely by asset. DOGE moves from 0.648 to 0.579, BTC from 0.301 to 0.278, and BNB from 0.348 to 0.342. We did not find per-asset significance tests. BNB's gap of 0.006 therefore carries no inference of its own. The test covers about two years, still one regime.

The benchmarks use the same data, though the machinery differs. NRM puts a neural layer and a hyperparameter grid above linear heads; the authors acknowledge the different parameter counts. Fixed-rule alternatives leave a sharper question. In the SHAP plots, locally small RV contributions tend to receive higher scores, while locally elevated contributions generally receive lower ones. Truncated RV or MedRV performs a similar operation without training. Of the compared primitives, only bipower variation resists jumps. We did not find benchmarks using truncated RV or MedRV.

The simulation warrants care. With jumps, contemporaneous RV has relative RMSE of 0.138, comparing 4.820 against 0.665 in units of 1e-5. The authors attribute that small ratio both to lower NRM error and to inflated RRM error from an estimand mismatch. The oracle excludes jumps; the raw measure includes them. With continuous diffusion, GK reaches only 0.976. For next-day forecasts in the continuous regime, the ratios are RV 0.919, BV 0.981 and GK 0.943. These simulations target latent integrated variance. The market exercise instead targets realized variance, which the authors describe as a noisy proxy.

Clock time carries the most weight

Removing Time from the HAR ablation increases QLIKE by 4.54%. Removing Local adds 4.01%, Global 2.54% and Shape 1.11%. GK loses 7.56% when Local is removed. BV actually improves by 0.48% without Shape.

Time leads even in a 24/7 market. For BTC, ETH and SOL RV, the SF-NRM profiles assign less weight to the middle of the UTC day and more to its start, especially its end. The authors warn that the UTC boundary or forecast origin may explain this pattern. Giving more weight to late bars fits a forecast-origin explanation: those observations are closest to tomorrow. The extra weight on early bars does not fit that account. These mechanism plots use a single seed-11 fit on three assets, limited to RV.

We did not run this method.

Its definition requires five-minute OHLC bars for these coins. We would need to rebuild them from one-minute data, check UTC alignment and filter for complete days. An equities implementation would test transfer to session markets, which the authors identify as unestablished. A volatility-targeted backtest would test an application they never claimed.

That backtest would supply the missing bridge. If NRM-sized books beat HAR-RRM on net Sharpe across these six coins, I would move toward the QLIKE headline.