Open Access
May 2007 A recursive online algorithm for the estimation of time-varying ARCH parameters
Rainer Dahlhaus, Suhasini Subba Rao
Bernoulli 13(2): 389-422 (May 2007). DOI: 10.3150/07-BEJ5009


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.


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Rainer Dahlhaus. Suhasini Subba Rao. "A recursive online algorithm for the estimation of time-varying ARCH parameters." Bernoulli 13 (2) 389 - 422, May 2007.


Published: May 2007
First available in Project Euclid: 18 May 2007

zbMATH: 1127.62078
MathSciNet: MR2331257
Digital Object Identifier: 10.3150/07-BEJ5009

Keywords: Locally stationary , recursive online algorithms , time-varying ARCH process

Rights: Copyright © 2007 Bernoulli Society for Mathematical Statistics and Probability

Vol.13 • No. 2 • May 2007
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