χ-Space: A Statistical-Spectral Approach for Characterizing Extreme Fluctuation Patterns in Time Series

The characterization of extreme events (XE) from time series has witnessed an increase of interest due to the great observational occurrence found in several fields, such as space and environmental physics. Motivated by this challenge, we propose a new parameter space (namely, [Formula: see text]-space) composed of two attributes that identify different classes of extreme fluctuations in a time series. Based on reformulated measures for statistical quantiles and singularity spectra, the distance from the origin in the [Formula: see text]-space characterizes the escape from Gaussianity and monofractality that occurs when extreme fluctuations are present in a time series. To generate time series with different patterns of extreme fluctuations, two canonical systems were carefully chosen as illustrative examples: the so-called p-model for multifractal extreme dissipation and the driven Lorenz chaotic model within an appropriate parameterization scheme. The results show that the investigated attributes can compose a two-dimensional space in which the patterns of extreme endogenous and exogenous fluctuations are distinguished with great precision. The characterization of some observed fluctuation patterns from space and environmental physics is presented as a case of practical application.