Funding Rate Predictability: Comparing OU, ARIMA, and Regime-Switching Models

Abstract#

Perpetual funding rates are the central pricing signal in crypto derivatives: the periodic payment that pins a perp to spot. If the funding rate is predictable even modestly, that predictability is directly monetizable — via delta-hedged funding carry, timing of entry into cash-and-carry baskets, or routing of basis trades. We test three model classes on 944,150 funding observations spanning 230 markets captured by the PerpsTrader system over a 7.02-day window (2026-06-06 to 2026-06-13): an Ornstein–Uhlenbeck mean-reversion process (AR(1)), an AIC-selected ARIMA-class autoregression (AR(p)), and a self-exciting threshold autoregressive regime-switching model (SETAR). Using an expanding-window walk-forward design with Diebold–Mariano significance tests, we find that mean reversion helps marginally on majors but the naive random walk is competitive or superior across the panel, that AR(1) parsimony dominates (order selection picks p=1 on 10 of 12 assets), and that regime-switching complexity is significantly worse more often than it is better. The funding rate is, at the 15-minute polling cadence, closer to a martingale than a mean-reverting process.

Hypotheses#

• H1 (mean reversion helps): Confidence 0.55. An OU/AR(1) model outperforms a naive random-walk forecast on out-of-sample RMSE. — Weakly supported on majors, refuted at panel level.
• H2 (parsimony dominates): Confidence 0.75. AIC-selected AR(p) rarely chooses orders above p=1, and higher-order models do not significantly beat AR(1). — Supported.
• H3 (regime-switching earns its complexity): Confidence 0.30. A two-regime SETAR significantly outperforms the linear AR model on a meaningful fraction of assets. — Refuted.

Data Provenance#

The funding rate field is the exchange-quoted premium-index funding rate (annualized). Funding settles on a conventional 8-hour cadence; between settlements the quoted value is a forward TWAP estimate that drifts smoothly toward the realized rate. No backtest PnL or risk-adjusted return figures are reported in this study — only forecast-error statistics — because execution cost, slippage, and funding-payment timing are not modeled here and a return-based metric without those costs would be misleading.

Methodology#

Each asset series is resampled to a 15-minute regular grid (4,105 raw polls → 674 grid points). The first 60% of each series is a fitting warmup; the remaining 40% (269 out-of-sample steps) is forecast one step ahead. Models are re-fit every 24 steps (~6 h) on an expanding window. The three contenders:

Ornstein–Uhlenbeck (AR(1) mean reversion). Discretized, the OU process is rₜ = c + φ·rₜ₋₁ + ε, with φ = exp(−θΔt). We estimate φ by OLS and recover the mean-reversion speed θ = −ln(φ)/Δt and half-life ln(2)/θ. This is the canonical "funding mean-reverts" model.

ARIMA-class (AR(p) with AIC order selection). We fit AR(p) for p=1..6 by OLS and select the order minimizing AIC. For stationary funding rates (d=0), this is the ARIMA(p,0,0) sub-class. We do not fit MA terms — a deliberate scope limitation (see Limitations).

Regime-switching (SETAR). A self-exciting threshold autoregressive model: the series is split into two regimes by a threshold on its own lag-1 value, with a separate AR(2)+intercept fit in each regime. The threshold is chosen by grid search over the 15th–85th percentiles to minimize in-sample SSE. This captures the intuition that funding behaves differently in calm vs. stressed regimes.

The baseline is a naive random walk (forecast = last observed value). Equal-forecast-accuracy is tested pairwise with the Diebold–Mariano statistic under absolute-error loss, using a Newey–West (lag-1) variance estimator.

# Diebold-Mariano under absolute-error loss, Newey-West(1)
def dm_test(e1, e2):
    d = np.abs(e1) - np.abs(e2)
    n = len(d)
    g0 = np.var(d, ddof=1)
    g1 = np.cov(d[1:], d[:-1], ddof=1)[0, 1] if n > 2 else 0.0
    var = g0 + 2 * g1                 # Newey-West with lag truncation 1
    stat = d.mean() / np.sqrt(var / n)
    p = 2 * (1 - norm.cdf(abs(stat)))
    return stat, p

# OU half-life from the AR(1) coefficient
theta = -np.log(phi) / dt             # mean-reversion speed
half_life = np.log(2) / theta         # in time units

Results#

Out-of-sample RMSE (in basis points of the annualized rate), best model per row in bold, and the Diebold–Mariano statistic for SETAR vs. AR (negative ⇒ SETAR better):

Panel means (bps RMSE): Naive 67.0 < AR 68.2 < OU 69.3 < SETAR 71.4.

What the numbers say#

1. The funding rate is close to a random walk at this cadence. The naive baseline has the lowest panel-mean RMSE. It is outright best on the two most volatile names (TRUMP, HYPE) and within noise of the leaders everywhere except BTC/DOGE/LTC. Mean reversion exists — the OU half-lives of 0.5–4.0 h are real and interpretable — but it is weak enough that a persistence forecast is hard to beat once you account for the flat stretches where the rate barely moves.

2. Parsimony dominates. AIC chose AR(1) on 10 of 12 assets; only ETH and ADA warranted AR(2). The one case where a higher-order model was significantly better than AR(1) is ADA (DM=3.70, p=0.0002), where a second lag captures mild oscillatory structure. Everywhere else, adding lags buys nothing.

3. Regime-switching rarely pays — and frequently backfires. SETAR was the per-asset best on only 4/12. Of those, only AVAX was a significant win (DM=−2.64, p=0.008); BNB was marginal (p=0.081). Meanwhile SETAR was significantly worse than the linear AR on four assets — SOL (p=0.002), DOGE (p<0.001), XRP (p=0.026), TRUMP (p=0.013). When the DM test can tell the models apart, it more often penalizes the nonlinear model than rewards it. The two-regime machinery fits noise it cannot forecast.

4. MAE tells an even blunter story. By mean absolute error, the naive baseline beats every model on BTC (13.2 bps vs OU's 15.6), DOGE, ADA, HYPE, and LTC. The models improve RMSE — they reduce the large errors — but cannot beat persistence on the typical, small step. This is the signature of a series that is mostly flat with occasional jumps: a martingale with fat-tailed increments.

Discussion#

Robust (high confidence): The naive random walk is a legitimate, hard-to-beat baseline for funding-rate forecasting at intraday cadence; any model claiming edge must clear it out-of-sample. Parsimony is real — AR(1) is the right default. The OU half-life (median ~1.4 h, range 0.5–4.0 h) is a useful summary statistic but should be treated as a point estimate in the current regime, not a structural constant.

Preliminary (moderate confidence): Mean reversion provides a small, genuine edge on the largest, most liquid majors (BTC, DOGE, LTC show OU ahead of naive on RMSE by 2–3%). This is consistent with funding being a smoother TWAP estimate on deep markets. The effect is small and evaporates under MAE on some names.

Not supported: H3 is refuted — two-regime SETAR does not systematically beat the linear model. Where funding does have higher-order structure (ADA), a plain AR(2) captures it more cheaply than a regime split. Nonlinear regime models are not justified for this signal at this frequency.

Limitations#

The central limitation is sample breadth: 7.02 days is a single market regime, captured at one polling cadence. A model ranking that holds in a quiet week can invert in a stress event; the OU half-lives and SETAR thresholds are explicitly marked UNRELIABLE as generalizations because they are window-sensitive and estimated from a single, calm regime with no funding shock to define a "stressed" regime. The AR(1) coefficients are well-identified (405+ training points each) and marked RELIABLE, but their stability over time is untested. We resample raw ~2.5-min polls to a 15-minute grid; the choice of grid and forward-fill interpolation affects the serial correlation the models exploit, and a coarser (hourly) grid or finer (tick) grid could change the ranking. We model only the quoted funding rate, not realized settlement payments or the premium index components. MA terms and integrated ARIMA structures are out of scope, so the "ARIMA-class" comparison is really AR(p) vs AR(1) vs SETAR — a fair but incomplete contest. Results are drawn from a single consolidated funding feed and should not be generalized to other exchanges or venues without re-validation; venues differ in settlement cadence, clamp bounds, and premium-index construction (e.g., funding on venues like Binance and Hyperliquid is not mechanically identical), and cross-exchange basis dynamics observed elsewhere are absent from this single-source sample. The panel of 12 assets is concentrated in majors; the long tail of 230 tracked markets (including illiquid names where funding is far more volatile) may behave very differently. Finally, no execution costs are modeled, so any forecast edge reported here is an upper bound on tradable edge.

Conclusion#

For delta-hedged funding strategies and basis timing, the practical implication is sobering: the quoted funding rate is approximately a martingale at intraday horizons, a simple AR(1) mean-reversion model captures essentially all the available structure, and the added complexity of regime-switching models is a net negative more often than a net positive on this sample. Deploying a SETAR or HMM over an AR(1) for funding-rate forecasting is not justified without evidence it clears the random-walk baseline out-of-sample in the regime you intend to trade. The honest engineering default is AR(1) with a naive-walk guard; spend modeling effort on the realized carry (settlement, execution, basis) rather than on the forecast of the quoted number. The remaining open question — whether predictability rises at the 8-hour settlement boundary where the rate converges to a realized payment — requires a longer, regime-diverse sample and is the natural next experiment.

References#

1. Diebold, F.X. & Mariano, R.S. (1995). Comparing Predictive Accuracy. Journal of Business & Economic Statistics.
2. Tong, H. (1978). On a Threshold Model. Pattern Recognition and Signal Processing.
3. Hansen, B.E. (1997). Inference in TAR Models. Studies in Nonlinear Dynamics & Econometrics.
4. Hull, J. (2018). Options, Futures, and Other Derivatives — funding-rate mechanics for perpetual contracts.
5. Venym Labs internal data: PerpsTrader funding database, 2026-06-06 to 2026-06-13.