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math.ST updates on arXiv.org

What is Learnable in Valiant's Theory of the Learnable? 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A recursive online algorithm for the estimation of time-varying ARCH parameters
Rainer Dahlhaus, Suhasini Subba Rao · 2007-08-30 · via math.ST updates on arXiv.org

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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