## Self-Similarity and Long-Range Dependence Through the Wavelet Lens (2000)

Citations: | 43 - 7 self |

### BibTeX

@MISC{Abry00self-similarityand,

author = {P. Abry and P. Flandrin and M. S. Taqqu and D. Veitch},

title = {Self-Similarity and Long-Range Dependence Through the Wavelet Lens},

year = {2000}

}

### Years of Citing Articles

### OpenURL

### Abstract

Self-similar and long-range dependent processes are the most important kinds of random processes possessing scale invariance. We describe how to analyze them using the discrete wavelet transform. We have chosen a didactic approach, useful to practitioners. Focusing on the Discrete Wavelet Transform, we describe the nature of the wavelet coefficients and their statistical properties. Pitfalls in understanding and key features are highlighted and we sketch some proofs to provide additional insight. The Logscale Diagram is introduced as a natural means to study scaling data and we show how it can be used to obtain unbiased semi-parametric estimates of the scaling exponent. We then focus on the case of long-range dependence and address the problem of defining a lower cutoff scale corresponding to where scaling starts. We also discuss some related problems arising from the application of wavelet analysis to discrete time series. Numerical examples using many discrete time models are th...