Journal of Economic Theory and Econometrics: Journal of the Korean Econometric Society
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Journal of Economic Theory and Econometrics
JETEM/계량경제학보/計量經濟學報/JKES
Journal of the Korean Econometric Society

On the Spectral Degeneracy of Wavelet Transforms of Fractional Brownian Motion

Vol.25, No.1, March , 58–66



  •   (Department of Economics, Ewha Womans University)

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Abstract  

Existence of spectral density of wavelet transform in the case of fractional Brownian motion is proved by Kato and Masry (1999). Given their results, we provide supplementary results on spectral behavior at the zero frequency. It is found that the spectral density at the zero frequency, determined by the memory parameter and the number of vanishing moments of the wavelets, generates possible degeneracy. Our results can be understood as spectral version of decorrelation properties of wavelet transforms.


Keywords
   Fractional Brownian Motion, Wavelet Transform, Spectral Density at the Zero Frequency, Degeneracy

JEL classification codes
   C12, C14
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