On the online estimation of local constant volatilities

Time varying volatilities in financial time series are commonly modeled by GARCH or by stochastic volatility models. Models with piecewise constant volatilities have been proposed recently as nonparametric alternatives. Following the latter approach, a procedure for online approximation of the current volatility is constructed by combining one-sided localized estimation of the variability with sequential testing for a change in it. A robust nonparametric framework is assumed since many financial time series show tails heavier than the Gaussian. A two-sample test for a change in variability is proposed, which works well even in case of skewed distributions.