ABSTRACT · 156 WORDS
The mechanism helps point forecasts; it does not repair every predictive distribution.
Perpetual-futures funding is a deterministic transformation of a kernel-weighted premium integral, yet the integral is rarely used as the state variable in next-settlement forecasts. We derive exact discrete moments and clamped-normal predictive distributions under an Ornstein–Uhlenbeck premium model, then evaluate genuinely out-of-sample forecasts for BTC, ETH, and SOL on Binance, Gate, and Hyperliquid. The 38-day public-data sample contains 2,781 targets over 31 evaluation days. OU reduces pooled RMSE from 0.2368 bp for the last-settlement benchmark to 0.1968 bp, but remains slightly behind EWMA at 0.1947 bp. Improvements over Last are strongest on Hyperliquid; Binance and Gate favor EWMA over OU. Minute-level reconstruction supports linear rather than equal kernels on Binance and Gate. Twenty configurations and Holm/Reality-Check procedures address selection. Gaussian intervals fail by venue: 95% coverage is 39.1%, 43.5%, and 97.7%, respectively. The evidence supports mechanism-aware point forecasting, not uniformly superior accuracy, calibrated uncertainty, or executable net returns.
阅读中文摘要
中文摘要
永续合约资金费是加权溢价积分经过确定性变换后的结果，但既有预测通常没有直接把这一积分作为状态变量。本文在 Ornstein–Uhlenbeck（OU）溢价模型下推导下一结算区间的精确离散矩与截断正态预测分布，并对 Binance、Gate 和 Hyperliquid 上的 BTC、ETH、SOL 进行真正的滚动样本外检验。公开数据覆盖 2026 年 9 月 24 日至 10 月 31 日，共 38 天；样本外评估覆盖 10 月的 31 天，包含 2,781 个下一期结算目标。分钟级重构结果支持 Binance 与 Gate 使用线性递增权重，而非等权重。
OU 的合并 RMSE 为 0.1968 bp，低于 Last 的 0.2368 bp，但略高于 EWMA 的 0.1947 bp；合并 MAE 最低，为 0.0836 bp。相对 Last 的改善在三场所均出现，且在 Hyperliquid 最明显；Binance 与 Gate 的 RMSE 则由 EWMA 更低。完整搜索包含 20 种配置，27 次 DM 比较统一采用 Holm 校正。Binance、Gate、Hyperliquid 的 95% 区间覆盖率分别为 39.1%、43.5% 和 97.7%，不支持通用校准结论。示例完整往返成本为 33.01 bp，不是净收益回测。结果支持机制感知的短期点预测，不支持“普遍更准确”“不确定性已校准”或“存在可执行净收益”的结论。
下载一页中文摘要 PDFI · RESEARCH QUESTION
Can the state that determines funding also improve its next-settlement forecast?
Funding is often forecast from previous settlements alone. Yet the venue mechanism first aggregates future premiums through a kernel and then applies a dead zone and caps. This paper asks whether an OU model of that premium state yields useful out-of-sample forecasts, and whether its Gaussian uncertainty remains credible after the same transformation.
Mechanism before reduced form
Reconstruct the integral with venue-specific kernels, then forecast its conditional moments rather than ignoring the settlement accounting.
Point loss and probability are separate
A lower RMSE does not imply calibrated coverage. Proper scores, PIT, and interval tests are reported alongside point errors.
Prediction is not net carry
Research 01 and 02 supply the cost, depth, transfer, and liquidation layers. This paper evaluates only the next-settlement forecast layer.
II · METHODS & DATA
Exact discrete moments pass through a monotone funding transformation.
On the observation grid, the premium follows an exact discrete AR(1) obtained from an OU state model. If the next interval contains steps j = 1, …, n with normalized kernel weights wj, the conditional integral mean and variance are computed without simulation.
μA = θ + (p0 − θ) Σ wjφj
Hn = wn, Hj = wj + φHj+1; σA2 = σε2 Σ Hj2
The point forecast is the expectation after the interest-rate dead zone and caps, not the transform evaluated at the mean. Quantiles use monotonicity; CRPS uses quantile-loss quadrature; the logarithmic score and randomized PIT use the mixed law with point masses. The main research example uses a 168-hour rolling window, empirical-Bayes logit-persistence shrinkage, raw persistence, and native kernels. These are disclosed research examples, not production settings.
| Venue | Native grid & kernel | Premium coverage per asset | OOS targets per asset |
|---|---|---|---|
| Binance | Minute · linear | 51,840 / 54,720 · 94.74% | 92 |
| Gate | Minute · linear | 54,666 / 54,720 · 99.90% | 92 |
| Hyperliquid | Hourly · equal | 912 / 912 · 100% | 743 |
Source: public venue archives and endpoints, 24 September–31 October 2026; snapshot acquired 3 November 2026. Missing public observations remain missing. One basis point (bp) equals 0.0001 in rate units.
III · MAIN RESULTS
OU improves on Last across venues, but EWMA remains ahead on the two minute-linear venues.
The pooled OU RMSE is 16.9% below Last, while its MAE is the lowest of the four models. The ranking changes by venue: Hyperliquid favors OU over both Last and EWMA; Binance and Gate favor EWMA on RMSE. Pooling therefore summarizes target-level loss, not a universal venue ranking.
| Venue | Model | MAE (bp) | RMSE (bp) |
|---|---|---|---|
| Binance | OU | 0.3591 | 0.4747 |
| EWMA | 0.3504 | 0.4638 | |
| Last | 0.4272 | 0.5722 | |
| Interest | 0.6262 | 0.7842 | |
| Gate | OU | 0.2894 | 0.3866 |
| EWMA | 0.2840 | 0.3703 | |
| Last | 0.3511 | 0.4554 | |
| Interest | 0.7149 | 0.8206 | |
| Hyperliquid | OU | 0.0240 | 0.0437 |
| EWMA | 0.0334 | 0.0604 | |
| Last | 0.0317 | 0.0611 | |
| Interest | 0.0387 | 0.0813 | |
| Pooled | OU | 0.0836 | 0.1968 |
| EWMA | 0.0898 | 0.1947 | |
| Last | 0.1027 | 0.2368 | |
| Interest | 0.1641 | 0.3649 |
Source: walk-forward forecasts, 1–31 October 2026. Lower MAE and RMSE are better. Pooled rows weight every target equally; the complete nine-series table is in the paper and reproduction package.
Funding transformation and integration kernels. The dead zone and monotone clamp produce interest-rate and cap point masses. Source: public venue rules cited in the paper.
Linear weights reconstruct public settled funding more closely than equal weights on Binance and Gate. RMSE is in bp on a log scale. Source: public minute premiums and settlements, 24 September–31 October 2026.
Out-of-sample RMSE by venue and model, in bp. OU improves on Last across venues and on both Last and EWMA only on Hyperliquid. Source: 2,781 forecasts over 31 evaluation days.
Nominal versus empirical central coverage. The dashed line is perfect calibration. Binance and Gate undercover; Hyperliquid overcovers. Source: primary OU predictive intervals.
Randomized PIT histograms by venue; the dashed line is uniform density. Randomization is used only at point masses. Binance and Gate remain U-shaped; Hyperliquid is closer to uniform but intervals overcover.
Pooled RMSE across all 20 configurations. The primary specification is purple; forced-kernel checks are grey. The minimum is a searched result, not independent confirmation of a deployment model.
IV · EVALUATION & ROBUSTNESS
Statistical significance is selective, and calibration fails differently by venue.
OU’s CRPS is 0.0682 bp and its pooled log score is −4.4478. These aggregate numbers conceal severe venue heterogeneity. Binance and Gate have 95% coverage of only 39.1% and 43.5%; Hyperliquid covers 97.7% but its 50% and 80% intervals also overcover. Pooled 80% coverage is 80.5%, yet violations are strongly dependent, so the near-nominal average is not a calibration defense.
| Venue | CRPS (bp) | Log score | 50% coverage | 80% coverage | 95% coverage |
|---|---|---|---|---|---|
| Binance | 0.3054 | −1.551 | 16.3% | 29.0% | 39.1% |
| Gate | 0.2483 | 0.079 | 18.8% | 29.7% | 43.5% |
| Hyperliquid | 0.0166 | −5.367 | 80.6% | 93.2% | 97.7% |
| Pooled | 0.0682 | −4.448 | 68.1% | 80.5% | 86.5% |
Four comparisons against Last or EWMA survive Holm
Binance SOL versus Last; Hyperliquid BTC and SOL versus Last; and Hyperliquid SOL versus EWMA. No Binance or Gate comparison against EWMA survives correction across all 27 tests.
The searched family improves on Last
White’s Reality Check covers 20 configurations, 31 days, and 2,000 circular-block bootstrap replications. The p-value is 0.00050. Its benchmark is Last—not EWMA.
Shorter examples have lower pooled RMSE
Ranges are 0.19319–0.19599 bp at 72 hours, 0.19666–0.19683 at 168 hours, and 0.19856–0.19859 at 336 hours. The main narrative stays with the primary 168-hour example.
The point-loss direction is stable
OU beats Last and has lower MAE than EWMA in both October halves, but does not clearly beat EWMA on pooled RMSE. Venue rankings remain the more important split.
Reconstruction and forecasting answer different questions
Wrong kernels materially damage retrospective settlement reconstruction but can have little pooled forecasting effect after mean reversion and the dead zone compress the integral.
Small error reductions are not trading returns
The illustrative 33.01 bp round-trip allowance equals $33.01 per $10,000 notional. It includes fees, spread, impact, transfer/time, and borrow assumptions, but no executable order-book P&L.
V · EVIDENCE BOUNDARIES
What this paper does not claim is part of the result.
No uniform accuracy claim
OU does not uniformly outperform EWMA. It is slightly behind EWMA on pooled RMSE and on Binance and Gate.
No universal probability calibration
The Gaussian law undercovers at minute-linear venues and overcovers on Hyperliquid. Near-nominal pooled 80% coverage is an averaging artifact.
No independent best-model confirmation
The 72-hour minimum comes from the same 20-model search family. It is not presented as a separately validated production choice.
No executable net-return estimate
No order-book walk, fee-tier observation, borrow quote, transfer path, position rule, leverage, or liquidation simulation is used.
No broad market generalization
Thirty-eight days and nine continuously observable series do not establish performance across other regimes, contracts, or venue rules.
No production disclosure
All numerical settings are public research examples. The page contains no production parameters, private interfaces, internal rules, credentials, or user data.
10.5281/zenodo.23868361 ↗RESEARCH 02Framing Net Carry for Cross-Venue Perpetual Funding Positions10.5281/zenodo.23897013 ↗Relationship: Research 06 evaluates the next-settlement forecast layer. Research 01 and 02 remain necessary for executable costs, depth, funding cash accounting, transfer constraints, and liquidation risk.
VI · LIMITATIONS
A short public-data snapshot cannot settle regime, archive, or execution uncertainty.
- Sample span. The 38-day sample contains one calendar month of evaluation. Premium persistence, volatility, and funding regimes can change.
- Venue and contract scope. Nine liquid, continuously observable series do not establish a broader universe free of survivorship bias.
- Public-input approximation. Minute and hourly archives need not reproduce native impact-price inputs or five-second venue sampling exactly.
- Missing archives. Two Binance daily archives per asset remain missing; no synthetic premiums are inserted.
- Model uncertainty. Gaussian OU omits parameter uncertainty, stochastic volatility, jumps, archive uncertainty, and model-selection uncertainty.
- Dependence. Assets and venues share market conditions; pooled target counts are not independent replications.
- Economic inputs. Complete net-return evaluation requires timestamped depth, actual fee tiers, borrow availability, transfer constraints, margin rules, and a predeclared position rule.
VII · CONCLUSION
Use the premium integral as a forecasting state—not as a promise of accuracy or profit.
The premium-integral mechanism adds useful structure to next-settlement point forecasting. OU improves on Last across all three venues and is strongest on Hyperliquid, while EWMA remains a serious benchmark and leads on Binance and Gate. The probability results reject a universal calibrated Gaussian law. The defensible contribution is therefore a mechanism-aware, reproducible forecast evaluation with explicit statistical and economic boundaries.
Mechanism-aware point evidence is supported. Uniform superiority, universal calibration, and executable net returns are not.
VIII · DOWNLOADS & CITATION
Paper, data, code, and citation.
Liu, H. (2026). Forecasting next-settlement funding from the premium integral: Mechanism-based Ornstein–Uhlenbeck evidence across three venues [Preprint]. humarb Research. https://doi.org/10.5281/zenodo.23918114
Cite the concept DOI 10.5281/zenodo.23918114; the version DOI 10.5281/zenodo.23918115 identifies v1.
Not investment advice. This page and paper are for research and methodological information only. They do not recommend a trade or position, do not promise accuracy or profit, and do not provide investment, legal, accounting, or tax advice. Historical estimates and illustrative costs can differ materially from actual execution, funding, borrowing, margin, and liquidation outcomes.