Tracking of Historical Volatility

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We propose an adaptive algorithm for tracking of historical volatility. The algorithm is built under the assumption that the historical volatility function belongs to the Stone-Ibragimov-Khasminskii class of $k$ times differentiable functions with bounded highest derivative and its subclass of functions satisfying a differential inequalities. We construct an estimator of the Kalman filter type and show optimality of the estimator's convergence rate to zero as sample size $n\to\infty$. This estimator is in the framework of GARCH design, but a tuning procedure of its parameters is faster than with traditional GARCH techniques.
20 pages, 4 figures

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Probability, Optimization and Control, Statistics Theory, 60G35, 60G51, 62G05, 62M20, 91B70

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http://salesiana.dossiersoluciones.com/handle/123456789/130542

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0404277
 http://arxiv.org/abs/math/0404277

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arXiv