Let $\{X_n\}_{n\ge0}$ be a sequence of real valued random variables such that $X_n=ρ_n X_{n-1}+ε_n,~n=1,2,\ldots$, where $\{(ρ_n,ε_n)\}_{n\ge1}$ are i.i.d. and independent of initial value (possibly random) $X_0$. In this paper it is shown that, under some natural conditions on the distribution of $(ρ_1,ε_1)$, the sequence $\{X_n\}_{n\ge0}$ is regenerative in the sense that it could be broken up into i.i.d. components. Further, when $ρ_1$ and $ε_1$ are independent, we construct a non-parametric strongly consistent estimator of the characteristic functions of $ρ_1$ and $ε_1$.