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HAAR-FISZ Technique for locally stationary volatility estimation
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When
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2.00pm on Friday 10th March
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Where
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B617, Leverhulme Library, Columbia House
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Presentations
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Speaker
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Piotr Fryzlewicz
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From
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Bristol University
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Abstract
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We consider a locally stationary model for financial log-returns whereby the returns are independent and the volatility is a piecewise constant function with an unknown number and location of jumps, defined on a compact interval to enable a meaningful estimation theory. We demonstrate that the model explains well the common stylised facts of log-returns. We propose a new wavelet thresholding algorithm for volatility estimation in this model, where Haar wavelets are combined with the variance-stabilizing Fisz transform. The resulting volatility estimator is mean-square consistent with a near-parametric rate, does not require any pre-estimates, is rapidly computable and easy to implement. We also discuss important variations on the choice of estimation parameters. We show that our approach both gives a very good fit to selected currency exchange datasets, and achieves accurate long- and short-term volatility forecasts in comparison to the GARCH (1,1) and moving window techniques.
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For further information
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Thomas Hewlett (Postgraduate Administrator) Ext. 6879
Department of Statistics, Columbia House
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