Abstract Traditional methods for the analysis of fractal time series are focused on obtaining the dynamical properties of the systems that gave rise to the signals. Some methods have been developed with the aim to identify power-law relationships that highlight scale invariance or fractal properties of the signals. These methodologies can identify temporal correlations, persistence, and even the fractal dimension associated with fluctuations in the time series. However, quantifying the complexity of a time series is a further challenge particularly for experimental signals, which in addition to being composed of deterministic and stochastic components, correspond to short sequences of data values. Usually the analysis of the stochastic component is focused on the statistical properties of the output variables, while for the deterministic components, the analysis is related to models of dynamical systems. The contributions in each value (deterministic and stochastic), as well as the temporal sequence of output values, contain information about the dynamics and the complexity of the time series. In addition to fractal features, the quantification of “complexity” of fractal time series has been the focus of considerable attention. Today, we have several meanings of complexity (see Chapter 8 where the issue of complexity is considered more broadly). In other words, there is not a well established universal definition of complexity to date [1] . For example, mathematical complexity has been defined as the length of the shortest binary input to a universal Turing machine such that the output is the initial string [2] , [3] . Nevertheless, the mathematical complexity of a system cannot be easily calculated. On the other hand, within the clinical domain, the meaning of complexity is associated with the presence of chaotic temporal variations in the steady state output [4] .