Hierarchical structures in Complex Systems: from DNA to financial markets

In this paper we discuss the concepts of short-range and long-range correlated stochastic processes and we investigate the presence of such variables in two model complex systems. The selected model systems are DNA sequences of complete genomes and financial time series of equities traded in a stock market. Specifically, by starting from our research results, we discuss the statistical properties of (i) coding and non-coding regions of DNA and (ii) equity returns and volatility in financial markets. The stylized facts about these variables are presented and discussed with a focus on the statistical tools already used and/or still needed to better characterize these model complex systems.