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A recursive online algorithm for the estimation of time-varying ARCH parameters. (English) Zbl 1127.62078

Summary: 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 a time point \(t-1\) with observations about the time point \(t\) to yield an estimator of the parameter at the 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.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62F10 Point estimation
65C60 Computational problems in statistics (MSC2010)
62M09 Non-Markovian processes: estimation
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