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A Haar-Fisz technique for locally stationary volatility estimation

By Piotr Fryzlewicz, Theofanis Sapatinas and Suhasini Subba Rao

Abstract

We consider a locally stationary model for financial log-returns whereby the returns are independent and the volatility is a piecewise-constant function with jumps of an unknown number and locations, defined on a compact interval to enable a meaningful estimation theory. We demonstrate that the model explains well the common characteristics of log-returns. We propose a new wavelet thresholding algorithm for volatility estimation in this model, in which Haar wavelets are combined with the variance-stabilising 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 is easily implemented. 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

Topics: HA Statistics
Publisher: Oxford University Press
Year: 2006
DOI identifier: 10.1093/biomet
OAI identifier: oai:eprints.lse.ac.uk:25225
Provided by: LSE Research Online
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