We propose a fully nonparametric empirical autoregressive copula framework for univariate time series, designed to capture nonlinear and asymmetric serial dependence while exactly preserving the empirical marginal distribution. The method decouples marginal behavior from temporal dependence by (i) constructing a shape-preserving empirical marginal via monotone interpolation and mapping observations to the unit interval, and (ii) estimating the lag--lead dependence through a nonparametric conditional AR(1) copula density on $(0,1)^2$. To ensure stable estimation near the boundaries, we employ reflection-based kernel methods that mitigate edge effects and yield well-behaved conditional densities on the unit support. Empirically, we evaluate the approach on three CBOE volatility indices (VIX, VXD, and RVX) and benchmark it against linear ARMA models, copula-based parametric competitors, and state-space / heteroskedasticity baselines (Local level, TVP--AR, and ARMA--GARCH). The results highlight that modeling the full conditional transition density nonparametrically can deliver competitive, often best or near-best, forecast accuracy across horizons.
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