Temperature time series analysis at Yucatan using natural and horizontal visibility algorithms.

Several methods to quantify the complexity of a time series have been proposed in the literature, which can be classified into three categories: structure/self-affinity, attractor in the phase space, and randomness. In 2009, Lacasa et al. proposed a new method for characterizing a time series called the natural visibility algorithm, which maps the data into a network. To further investigate the capabilities of this technique, in this work, we analyzed the monthly ambient temperature of 4 cities located in different climatic zones on the Peninsula of Yucatan, Mexico, using detrended fluctuation analysis (structure complexity), approximate entropy (randomness complexity) and the network approach. It was found that by measuring the complexity of the dynamics by structure or randomness, the magnitude was very similar between the cities in different climatic zones; however, by analyzing topological indices such as Laplacian energy and Shannon entropy to characterize networks, we found differences between those cities. With these results, we show that analysis using networks has considerable potential as a fourth way to quantify complexity and that it may be applied to more subtle complex systems such as physiological signals and their high impact on early warnings.