Abstract

A wavelet based statistical test is described for distinguishing true time variation of the scaling exponent describing scaling behaviour, from statistical fluctuations of estimates across time of a constant exponent. The test is applicable to diverse scaling phenomena including long range dependence and exactly selfsimilar processes in a uniform framework, without the need for prior knowledge of the type in question. It is based on the special properties of wavelet-based estimates of the scaling exponent over adjacent blocks of data, strongly motivating an idealised inference problem: the equality or otherwise of means of independent Gaussian variables with known variances. A uniformly most powerful invariant test exists for this problem and is described. A separate UMPI test is also described for when the scaling exponent undergoes a level change. The power functions of the two tests are given explicitly and compared. Using simulation the effect in practice of deviations from the ide...

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