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Biometrika 1995 82(2):385-397; doi:10.1093/biomet/82.2.385
© 1995 by Biometrika Trust
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Jump and sharp cusp detection by wavelets

YAZHEN WANG

Department of Statistics, University of Missouri-Columbia Columbia, Missouri 65211, U.S.A.

A method is proposed to detect jumps and sharp cusps in a function which is observed with noise, by checking if the wavelet transformation of the data has significantly large absolute values across fine scale levels. Asymptotic theory is established and practical implementation is discussed. The method is tested on simulated examples, and applied to stock market return data.

Key Words: Convergence rate • Estimation • Hypothesis • Jump • Nonparametric regression • Sharp cusp • Wavelet transformation • White noise • White noise model


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