Summary: The aggregation procedure is a natural way to analyse signals which exhibit long-range-dependent features and has been used as a basis for estimation of the Hurst parameter, . In this paper it is shown how aggregation can be naturally rephrased within the wavelet transform framework, being directly related to approximations of the signal in the sense of a Haar multiresolution analysis.
A natural wavelet-based generalization to traditional aggregation is then proposed: ‘a-aggregation’. It is shown that a-aggregation cannot lead to good estimators of , and so a new kind of aggregation, ‘d-aggregation’, is defined, which is related to the details rather than the approximations of a multiresolution analysis. An estimator of based on d-aggregation has excellent statistical and computational properties, whilst preserving the spirit of aggregation. The estimator is applied to telecommunications network data.