Abstract: We consider the nonlinear autoregressive model X_i=r_θ(X_i-1,…,X_i-s)+ε_i,, where θ is a q-dimensional unknown parameter, {ε_i} is an independent and identically distributed random error with a mean of zero, and a variance of σ². We give the Berry-Esseen bound for error density estimators in nonlinear autoregressive models under appropriate assumptions.

Key words: nonlinear autoregressive model, kernel density estimator, Berry-Esseen bound