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On the approximate decorrelation property of the discrete wavelet transform for fractionally differenced processes

机译：关于分数差分过程的离散小波变换的近似解相关性

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摘要

In this correspondence, we develop an asymptotic theory for the correlations of wavelet coefficients of the discrete wavelet transform (DWT) for fractionally differenced processes. It provides a theoretical justification for the approximate decorrelation property of the DWT for fractionally differenced processes. In addition, it provides insights on how the length of the wavelet filter affects the within scale correlations and the between scale correlations differently; for within scale correlations, increasing the length of the wavelet filter increases the rate of decay as the two wavelet coefficients get further apart, while for between scale correlations, using a wavelet filter that is long enough can reduce the between scale correlations even for wavelet coefficients that are close together.
机译：在这种对应关系中，我们为分数差分过程的离散小波变换（DWT）的小波系数的相关性开发了一种渐近理论。它为分数差分过程的DWT的近似解相关特性提供了理论依据。另外，它提供了关于小波滤波器的长度如何影响尺度内相关和尺度间相关的见解。对于尺度相关性，当两个小波系数进一步分开时，增加小波滤波器的长度会增加衰减率，而对于尺度相关性，即使对于小波系数，使用足够长的小波滤波器也可以减小尺度相关性之间的差靠在一起。

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