A Distribution-Free Neural Estimator for Mean Reversion, with Application to Energy Commodity Markets

Accurate estimation of the mean-reversion speed $\alpha$ in the AR(1) process $X_{t+1} = (1-\alpha)X_t + \varepsilon_t$ is central to energy-commodity modelling. Classical estimators such as GARCH, jump-diffusion, and regime-switching produce model-conditioned estimates by embedding $\alpha$ within distributional assumptions, so that different model choices yield different $\hat{\alpha}$ values from the same series without a principled criterion to adjudicate. We propose a distribution-free estimator based on a Temporal Convolutional Network (TCN) trained on synthetic AR(1) series with Sinh-ArcSinh innovations of varying tail weight and asymmetry. The SAS family serves as a training vehicle---not a distributional hypothesis---chosen for its ability to span innovation profiles from near-Gaussian to strongly leptokurtic and skewed through its tail-weight and asymmetry parameters. Because the autocorrelation structure $\rho_k = (1-\alpha)^k$ is invariant to the marginal innovation distribution (Yule-Walker invariance), the TCN learns to extract $\alpha$ from temporal dependence alone, independently of distributional assumptions. On held-out test series the estimator outperforms all three classical estimators across the training innovation kurtosis range, with the advantage growing monotonically with non-Gaussianity. A robustness analysis on three out-of-distribution innovation families confirms stable or improved performance well beyond the training boundary. The distribution-free $\hat{\alpha}$ enables a two-stage pipeline in which $\alpha$ and the innovation distribution are characterised independently---a decoupling structurally impossible in classical likelihood-based approaches. Once trained, the TCN acts as a universal mean-reversion estimator applicable to any price series without re-fitting. Applied to four energy markets---Italian natural gas (PSV price), Italian electricity (PUN price), US Henry Hub, and US PJM West Hub---spanning log-return kurtosis from near-Gaussian to strongly heavy-tailed, the TCN yields robust, model-free estimates not conditioned on any distributional hypothesis.