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.

Published at http://dx.doi.org/10.3150/07-BEJ5009 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

References in corpus (2)

• A recursive online algorithm for the estimation of time-varying ARCH parameters
• Phase synchronization from noisy univariate signals

Cited by in corpus (1)

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