Hurst Space Analysis – data discrimination tool based on cyclic trends in records

dr Suzana Blesić, Institute for Medical Research, Belgrade

Abstract: It was shown for variables across different complex systems that their fluctuation functions calculated with detrending methods of scaling analysis frequently exhibit existence of transient crossovers in behavior, signs of trends that arise as effects of periodic or aperiodic cycles. We recently developed a technique to cluster or differentiate records from an arbitrary complex system dataset based on the presence and influence of these cycles in data, which we dubbed the Hurst Space Analysis (HSA). We defined a space of -vectors that represent records in the dataset, which we called the Hurts space. Vectors are populated by scaling exponents calculated on subsets of time scale windows of time series that bound cyclic peaks in their global wavelet power spectra (WTSs), by way of use of time dependent detrended moving average analysis (tdDMA). The length depends on the number of WTS peaks in that complex system. This number is, as was shown across complex systems, universal. To be able to quantify any time series with a single number, we projected their relative Hurst space unit vectors (with ) onto a unit vector of an assigned preferred direction in the Hurst space. The definition of the ’preferred’ direction depends on the characteristic behavior one wants to investigate with HSA – projection of unit vectors of any record with a ’preferred’ behavior onto the unit vector will then always be positive.

The HSA procedure can serve to examine and differentiate records within datasets of randomly selected time series of any complex variable. We used HSA to differentiate complex time series of stock market data, based on the preferred characteristic of marked development, and to cluster datasets of observed temperature records from land stations from different climatically and topologically homogeneous regions, based on the ‘belonging to a continent’ preference.

Biography: Suzana Blesić is an assistant research professor at the Institute for Medical Research in Belgrade. She holds a PhD in theoretical statistical physics, a post-doc at CNRS Marseilles, has worked in laboratories in Sweden and Japan, and has led a Marie Curie research project at the Ca’Foscari University of Venice in Italy. She has explored disparate research fields – first neuroscience, then finance and now climate change – with two purposes: analyzing and understanding complex systems and developing methodological frameworks for (their) data analysis. Currently she leads a Group for Biomechanics, Biomedical Engineering and Physics of Complex Systems at her home institute. She is also a co-PI and a WP leader of the Horizon Europe project that will investigate relationships between vector borne diseases and climate and environmental change and develop preparedness tools for adaptation to that change.