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 $X_{t+1}=(1-\alpha )X_t+{\epsilon }_t$ 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 $\widehat{\alpha }$ values from the same series without a principled criterion to adjudicate. We propose a distribution-free neural estimator based on a Temporal Convolutional Network (TCN) trained on synthetic AR(1) series with Sinh-ArcSinh (SAS) innovations. Distribution-free here means that no parametric family is assumed for the innovation distribution at inference time: the estimator imposes no distributional hypothesis when processing a new series. The SAS family serves as a training vehicle—not a model for the real data—chosen for its ability to span a broad range of tail weights and asymmetry profiles. The theoretical foundation is spectral invariance: the Yule–Walker equations establish that the autocorrelation structure ${\rho }_k={(1-\alpha )}^k$ depends on $\alpha$ alone, provided innovations are uncorrelated across lags—a condition satisfied not only by i.i.d. innovations but also by conditionally heteroscedastic processes such as GARCH. The TCN therefore generalises to volatility-clustering environments without modification, learning to extract $\alpha$ from temporal dependence alone, independently of the marginal innovation distribution and of the temporal variance structure. On held-out test series the estimator outperforms all classical competitors, with the advantage growing monotonically with non-Gaussianity. A robustness analysis on three out-of-distribution innovation families and on AR(1)-GARCH(1,1) processes empirically validates the spectral invariance guarantee across both marginal and temporal variance structure, including near-integrated GARCH processes where innovation kurtosis far exceeds the training range. The distribution-free $\widehat{\alpha }$ 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, distribution-free estimates of mean-reversion speed.