We consider the problem of optimal adaptive estiamtion of the euclidean parameter vector $ heta$ of the univariate non-linerar autogressive time series model ${X_t}$ which is defined by the following system of stochastic difference equations ; $X_t = sum^p_{i=1} heta_i cdot T_i(X_{t-1})+e_t, t=1, cdots, n$, where $ heta$ is the unknown parameter vector which descrives the deterministic dynamics of the stochastic process ${X_t}$ and ${e_t}$ is the sequence of white noises with unknown density $f(cdot)$. Under some general growth conditions on $T_i(cdot)$ which guarantee ergodicity of the process, we construct a sequence of adaptive estimatros which is locally asymptotic minimax (LAM) efficient and also attains the least possible covariance matrix among all regular estimators for arbitrary symmetric density.