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We have proposed novel measures based on the Kolmogorov complexity for use incomplex system behavior studies and time series analysis. We have consideredbackground of the Kolmogorov complexity and also we have discussed meaning ofthe physical as well as other complexities. To get better insights into thecomplexity of complex systems and time series analysis we have introduced thethree novel measures based on the Kolmogorov complexity: (i) the Kolmogorovcomplexity spectrum, (ii) the Kolmogorov complexity spectrum highest value and(iii) the overall Kolmogorov complexity. The characteristics of these measureshave been tested using a generalized logistic equation. Finally, the proposedmeasures have been applied on different time series originating from: the modeloutput (the biochemical substance exchange in a multi-cell system), fourdifferent geophysical phenomena (dynamics of: river flow, long termprecipitation, indoor 222Rn concentration and UV radiation dose) and economy(stock prices dynamics). Results which are obtained offer deeper insights intocomplexity of the system dynamics behavior and time series analysis when theproposed complexity measures are applied.

Novel measures based on the Kolmogorov complexity for use in complex system behavior studies and time series analysis