Self-Similarity Index Estimation via Wavelets for Locally Self-Similar Processes

Introduction A self-similar process is loosely defined as a stochastic process which generates a sample path that retains the same general appearance regardless of the distance from which it is observed. Self-similarity is a pervasive characteristic in naturally occurring phenomena. As a result, self-similar processes have been used to successfully model data arising in a variety of different scientific fields, including hydrology, geophysics, biology, medicine, and economics. Self-similar processes were introduced to statisticians through the work of B. B. Mandelbrot (Mandelbrot & van Ness, 1968; Mandelbrot & Wallis, 1968, 1969). A stochastic process Y (t) is formally defined as self-similar if L(Y (c t)) = L(c H Y (t)) for c ? 0; where L denotes the finite joint distribution of<F29.