Wavelet-based estimators of scaling behavior

Various wavelet-based estimators of self-similarity or long-range dependence scaling exponent are studied extensively. These estimators mainly include the (bi)orthogonal wavelet estimators and the Wavelet Transform Modulus Maxima (WTMM) estimator. This study focuses both on short and long time-series. In the framework of Fractional Auto-Regressive Integrated Moving Average (FARIMA) processes, we advocate the use of approximately adapted wavelet estimators. For these "ideal" processes, the scaling behavior actually extends down to the smallest scale, i.e., the sampling period of the time series, if an adapted decomposition is used. But in practical situations, there generally exists a cut-off scale below which the scaling behavior no longer holds. We test the robustness of the set of wavelet-based estimators with respect to that cut-off scale as well as to the specific density of the underlying law of the process. In all situations the WTMM estimator is shown to be the best o...

• Type: Journal
• Year: 2002
• Where: TIT
• Authors: Benjamin Audit, E. Bacry, J.-F. Muzy, Alain Arneodo
• Keywords: Estimator, TIT 2002, Various Wavelet-based Estimators, Wavelet-based Estimators