Multifractal detrended fluctuation analysis of nonstationary time series

We develop a method for the multifractal characterization of nonstationary time series, which is based on a generalization of the detrended fluctuation analysis (DFA). We relate our multifractal DFA method to the standard partition function-based multifractal formalism, and prove that both approaches are equivalent for stationary signals with compact support. By analyzing several examples we show that the new method can reliably determine the multifractal scaling behavior of time series. By comparing the multifractal DFA results for original series to those for shuffled series we can distinguish multifractality due to long-range correlations from multifractality due to a broad probability density function. We also compare our results with the wavelet transform modulus maxima (WTMM) method, and show that the results are equivalent.Comment: 14 pages (RevTex) with 10 figures (eps

CAG repeat expansion in Huntington disease determines age at onset in a fully dominant fashion

Objective: Age at onset of diagnostic motor manifestations in Huntington disease (HD) is strongly correlated with an expanded CAG trinucleotide repeat. The length of the normal CAG repeat allele has been reported also to influence age at onset, in interaction with the expanded allele. Due to profound implications for disease mechanism and modification, we tested whether the normal allele, interaction between the expanded and normal alleles, or presence of a second expanded allele affects age at onset of HD motor signs. Methods: We modeled natural log-transformed age at onset as a function of CAG repeat lengths of expanded and normal alleles and their interaction by linear regression. Results: An apparently significant effect of interaction on age at motor onset among 4,068 subjects was dependent on a single outlier data point. A rigorous statistical analysis with a wellbehaved dataset that conformed to the fundamental assumptions of linear regression (e.g., constant variance and normally distributed error) revealed significance only for the expanded CAG repeat, with no effect of the normal CAG repeat. Ten subjects with 2 expanded alleles showed an age at motor onset consistent with the length of the larger expanded allele. Conclusions: Normal allele CAG length, interaction between expanded and normal alleles, and presence of a second expanded allele do not influence age at onset of motor manifestations, indicating that the rate of HD pathogenesis leading to motor diagnosis is determined by a completely dominant action of the longest expanded allele and as yet unidentified genetic or environmental factors. Copyright © 2012 by AAN Enterprises, Inc