  We propose an adaptive algorithm for tracking of historical volatility. The
algorithm is built under the assumption that the historical volatility function
belongs to the Stone-Ibragimov-Khasminskii class of $k$ times differentiable
functions with bounded highest derivative and its subclass of functions
satisfying a differential inequalities. We construct an estimator of the Kalman
filter type and show optimality of the estimator's convergence rate to zero as
sample size $n\to\infty$. This estimator is in the framework of GARCH design,
but a tuning procedure of its parameters is faster than with traditional GARCH
techniques.
