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A Haar-Fisz technique for locally stationary volatility estimation

Fryzlewicz, Piotr, Sapatinas, Theofanis and Subba Rao, Suhasini (2006) A Haar-Fisz technique for locally stationary volatility estimation. Biometrika, 93 (3). pp. 687-704. ISSN 0006-3444

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Identification Number: 10.1093/biomet/93.3.687


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.

Item Type: Article
Official URL:
Additional Information: © 2006 The Authors
Divisions: Statistics
Subjects: H Social Sciences > HA Statistics
Date Deposited: 18 Sep 2009 11:41
Last Modified: 20 Jul 2021 00:47

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