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Tracking volatility. (English. Russian original) Zbl 1201.91227

Probl. Inf. Transm. 41, No. 3, 212-229 (2005); translation from Probl. Peredachi Inf. 2005, No. 3, 32-50 (2005).
Summary: We propose an adaptive algorithm for tracking historical volatility. The algorithm borrows ideas from nonparametric statistics. In particular, we assume that the volatility is a several times differentiable function with a bounded highest derivative. We propose an adaptive algorithm with a Kalman filter structure, which guarantees the same asymptotics (well known from statistical inference) with respect to the sample size \(n\), \(n \rightarrow \infty\). The tuning procedure for this filter is simpler than for a GARCH filter.

MSC:

91G70 Statistical methods; risk measures
62M20 Inference from stochastic processes and prediction
65C60 Computational problems in statistics (MSC2010)
91G60 Numerical methods (including Monte Carlo methods)
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