  This paper focuses on recursive estimation of time varying autoregressive
processes in a nonparametric setting. The stability of the model is revisited
and uniform results are provided when the time-varying autoregressive
parameters belong to appropriate smoothness classes. An adequate normalization
for the correction term used in the recursive estimation procedure allows for
very mild assumptions on the innovations distributions. The rate of convergence
of the pointwise estimates is shown to be minimax in $\beta$-Lipschitz classes
for $0<\beta\leq1$. For $1<\beta\leq 2$, this property no longer holds. This
can be seen by using an asymptotic expansion of the estimation error. A bias
reduction method is then proposed for recovering the minimax rate.
