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Jump and sharp cusp detection by wavelets. (English) Zbl 0824.62031
Summary: 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.

MSC:
62G07 Density estimation
62G20 Asymptotic properties of nonparametric inference
62P20 Applications of statistics to economics
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