On spurious and corrupted multifractality: The effects of additive noise, short-term memory and periodic trends

We study the performance of multifractal detrended fluctuation analysis (MF-DFA) applied to long-term correlated and multifractal data records in the presence of additive white noise, short-term memory and periodicities. Such additions and disturbances that can be typically found in the observational records of various complex systems ranging from climate dynamics to physiology, network traffic, and finance. In monofractal records, we find that (i) additive white noise hardly results in spurious multifractality, but causes underestimated generalized Hurst exponents h ( q ) for all q values; (ii) short-range correlations lead to pronounced crossovers in the generalized fluctuation functions F q ( s ) at positions that decrease with increasing moment q , thus causing significantly overestimated h ( q ) for small q and spurious multifractality; (iii) periodicities like seasonal trends (with standard deviations comparable with the one of the studied process) result in spurious “reversed” multifractality where h ( q ) increases with increasing q (except for very short time windows). We also show that in multifractal cascades moderate additions of noise, short-range memory, or periodic trends cause flawed results for h ( q ) with q < 2 , while h ( q ) with q > 2 remains nearly unchanged.