Correlation of Data Series. A Scientific Study on the Selection of Meaningful Variables and Functions for the Separation of Trends, Cyclic Parts and Scatter from Data Series

Scientific Study from the year 2015 in the subject Mathematics - Applied Mathematics, , language: English, comment: Author: Hans-Martin Stoenner Own Work: 2011-2014 Review: 2015 by Dr. Gerhard Hochgesand, Dr. Jürgen Grieser, Carolina Stoenner The reviewers found the examples for the correlation methods so exiting, that they proposed to write an introduction into the examples even for readers not interested in the mathematics itself. And the philosophy behind the methods was also of great interest. More details see sections Preface and Conclusion., abstract: Originally, I wrote this essay for readers interested in the correlation of data series, supplemented by examples for the explanation of the proposed methods. I have shown several mathematical models and numerous figures, graphics and charts for better comprehension.During the preview of this essay the selected examples turned out to be so exciting, that a short introduction into the examples themselves would be advisable, also to readers not interested in mathematics and modeling: The increasing number of annual airport passengers was a good example for the fundamental question whether time or population causes this increase. For the rise of the atmospheric carbon dioxide content over long periods in between the present interglacial, I found an unrivaled variable for the correlation.For the growth of the world population from origin of Homo sapiens up to its growth limit, I compared two different models, one time-based, the other one population-based.For the long-term growth of Dow Jones Industrial Index, I found a good correlation with world population and time, while the long term volatility correlated fairly with time. The long-term climate change correlates with world population, whereas the long natural cyclic climate observations correlate with time, and the combination of both lead to pioneering innovative visualizations, again within the present interglacial.