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

Area of Science:

• Complex systems analysis
• Time series analysis
• Network science

Background:

• Existing time series complexity quantification methods fall into structure/self-affinity, phase space attractors, or randomness categories.
• The natural visibility algorithm (2009) maps time series data into a network, offering a novel approach to complexity analysis.

Purpose of the Study:

• To investigate the capabilities of the natural visibility algorithm for time series complexity analysis.
• To compare network-based complexity measures with traditional methods (detrended fluctuation analysis and approximate entropy) using ambient temperature data.
• To explore the potential of network analysis as a fourth method for quantifying complexity.

Main Methods:

• Analysis of monthly ambient temperature data from four cities in different climatic zones on the Yucatan Peninsula, Mexico.
• Application of detrended fluctuation analysis for structure complexity.
• Application of approximate entropy for randomness complexity.
• Characterization of time series networks using topological indices like Laplacian energy and Shannon entropy.

Main Results:

• Structure and randomness complexity measures showed similar magnitudes across cities in different climatic zones.
• Network analysis using topological indices revealed significant differences in complexity between the cities.
• The network approach demonstrated potential for detecting subtle variations not captured by traditional methods.

Conclusions:

• Network analysis, particularly using the natural visibility algorithm, offers a promising fourth dimension for quantifying time series complexity.
• This method can differentiate complex systems with subtle variations, such as physiological signals, potentially aiding in early warning systems.
• The study highlights the value of network-based approaches in uncovering hidden dynamics within complex data.