A recursive online algorithm for the estimation of time-varying ARCH parameters

Abstract

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 Hölder classes of order between 1 and 2. © 2007 ISI/BS.