Tracking the Volatility Function

We propose an adaptive algorithm for tracking historical volatility. The algorithm borrows ideas from nonparametric statistics. In particular, we assume that the volatility is a several times differentiable function with a bounded highest derivative. We propose an adaptive algorithm with a Kalman filter structure, which guarantees the same asymptotics (well known from statistical inference) with respect to the sample size $n$, $n\to\infty$. The tuning procedure for this filter is simpler than for a GARCH filter.