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 | Dataset | Source | Cadence | Window | Records | Reliability | |---|---|---|---|---|---| | Funding rates | PerpsTrader funding database (fundingrates table) | polled 2.46 min | 2026-06-06 → 2026-06-13 (7.02 d) | 944,150 | RELIABLE (raw, machine-collected) | | Analysis panel | 12 liquid markets (BTC, ETH, SOL, XRP, DOGE, LINK, BNB, ADA, AVAX, TRUMP, HYPE, LTC) | resampled 15-min grid | same | 674 obs/asset | RELIABLE (deterministic resample) | | OU half-lives | estimated from AR(1) coefficient | per-asset | 7-day window | 12 | UNRELIABLE (window-sensitive, single regime) | | SETAR thresholds | grid-searched on lag-1 quantiles | per-asset | 7-day window | 12 | UNRELIABLE (2-regime split unstable on 7 d) | 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. 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): | Asset | OU | AR(p) | SETAR | Naive | OU half-life (h) | AR order | DM(SET−AR), p | |---|---|---|---|---|---|---|---| | BTC | 25.3 | 25.3 | 25.5 | 25.9 | 1.28 | 1 | +0.13, 0.90 | | ETH | 36.1 | 35.8 | 35.7 | 36.9 | 1.49 | 2 | −1.02, 0.31 | | SOL | 42.6 | 42.6 | 43.0 | 42.6 | 4.01 | 1 | +3.14, 0.002 | | XRP | 39.5 | 39.5 | 40.6 | 40.6 | 1.70 | 1 | +2.22, 0.026 | | DOGE | 21.6 | 21.6 | 21.7 | 22.1 | 2.91 | 1 | +5.63, <0.001 |