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Nonlinear time series analysis in the geosciences

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The significant advancements in understanding the Earth as a complex system over recent decades are largely attributed to the availability of extensive data sets and advanced analytical methods. Univariate and multivariate time series data play a crucial role in examining dynamic processes within these systems. The interplay between time series analysis and applications in geo- and astrophysics has been historically enriching, beginning with classical linear problems like power spectrum estimation, notably advanced by Udny Yule in his studies of sunspot activity and later by John Tukey. As evidence mounted in the latter half of the 20th century that many natural processes are inherently non-linear, it became clear that linear statistical methods were insufficient. The emergence of dynamic systems theory, highlighted by Edward Lorenz’s groundbreaking work, alongside early fractal concepts introduced by Harold Edwin Hurst, facilitated the application of nonlinear methods to time series analysis. In recent decades, these methods have garnered increasing attention across various earth science disciplines. In response, prominent geoscientific organizations, such as the American Geophysical Union and the European Geosciences Union, have established specialized nonlinear focus groups and topical sections, actively participating in their respective annual meetings.

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Nonlinear time series analysis in the geosciences, Reik Donner

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2008
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