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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