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Time–Threshold Maps: Using information from wavelet reconstructions with all threshold values simultaneously

Fryzlewicz, Piotr (2012) Time–Threshold Maps: Using information from wavelet reconstructions with all threshold values simultaneously. Journal of the Korean Statistical Society, 41 (2). pp. 145-159. ISSN 1226-3192

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Abstract

Wavelets are a commonly used tool in science and technology. Often, their use involves applying a wavelet transform to the data, thresholding the coefficients and applying the inverse transform to obtain an estimate of the desired quantities. In this paper, we argue that it is often possible to gain more insight into the data by producing not just one, but many wavelet reconstructions using a range of threshold values and analysing the resulting object, which we term the Time-Threshold Map (TTM) of the input data. We discuss elementary properties of the TTM, in its "basic" and "derivative" versions, using both Haar and Unbalanced Haar wavelet families. We then show how the TTM can help in solving two statistical problems in the signal + noise model: breakpoint detection, and estimating the longest interval of approximate stationarity. We illustrate both applications with examples involving volatility of financial returns. We also briefly discuss other possible uses of the TTM.

Item Type: Article
Official URL: http://www.journals.elsevier.com/journal-of-the-ko...
Additional Information: © 2012 Korean Statistical Society
Library of Congress subject classification: H Social Sciences > HA Statistics
Sets: Departments > Statistics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 04 Apr 2012 14:29
URL: http://eprints.lse.ac.uk/43011/

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