  In this paper we propose a recursive online algorithm for estimating the
parameters of a time-varying ARCH process. The estimation is done by updating
the estimator at time point $t-1$ with observations about the time point $t$ to
yield an estimator of the parameter at time point $t$. The sampling properties
of this estimator are studied in a non-stationary context -- in particular,
asymptotic normality and an expression for the bias due to non-stationarity are
established. By running two recursive online algorithms in parallel with
different step sizes and taking a linear combination of the estimators, the
rate of convergence can be improved for parameter curves from H\"{o}lder
classes of order between 1 and 2.
