Suppose the $X_0,\dots, X_n$ are observations of a one-dimensional
stochastic dynamic process described by autoregression equations when the
autoregressive parameter is drifted with time, i.e. it is some function of
time: $\theta_0,\dots, \theta_n$, with $\theta_k = \theta(k/n)$. The function
$\theta(t)$ is assumed to belong a priori to a predetermined nonparametric
class of functions satisfying the Lipschitz smoothness condition. At each time
point $t$ those observations are accessible which have been obtained during the
preceding time interval. A recursive algorithm is proposed to estimate
$\theta(t)$.Under some conditions on the model,we derive the rate of
convergence of the proposed estimator when the frequencyof observations $n$
tends to infinity.