An algorithm for the characterization of time-series based on local regularity

The pointwise Holder exponent describes the local regularity of a function. This description is particularly applicable to complex time-series representing natural phenomena that exhibit statistical self-similarity, where the scaling exponent fluctuates from point to point. In this work, an algorithm is proposed for the estimation of both global and local scaling exponents of time-series. The technique is based on scaled window variance method and its practical implementation relies on the convolution operation. The proposed algorithm is an attractive alternative to existing techniques because of its simplicity and computational efficiency. The accuracy of the algorithm is verified by application on synthetic signals with a prescribed time evolution of Holder exponents. Case studies are presented in the fields of fluid dynamics, room acoustics and machinery diagnostics.