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.
Table of Contents
Preface
On the Correlation of Data Series
1 Selection of Meaningful Functions and Variables for the Analysis of Data Series
2 Examples for Separating Functions
2.1 Growth Functions
2.2 Other Methods like so called Filters
2.3 Useful functions for the steady part of the data series
2.4 Cyclic Components
2.5 Elimination of Scattered Points (Noise)
2.6 Overview on Separating Functions
2.6.1 Independent and additive trends and fluctuations
2.6.2 Dependent and multiplicative growth functions
2.6.3 Importance of Predictability
3 Examples for the proposed Method
3.1 Example One: World population time series
3.2 Example Two: Dow Jones Industrial Index
3.3 Example Three: World Climate Change
3.3.1 Description of Climate Separating Functions
3.3.2 Comparison of three different CRU time series
3.3.3 Attention
4 Conclusion
Objectives and Topics
This work proposes a mathematical method to analyze complex data series by separating long-term steady trends from cyclic oscillations and random noise. The primary research goal is to demonstrate that many seemingly chaotic data sets can be effectively correlated by shifting the focus from a time-based dependency to alternative variables, such as world population, thereby enabling more reliable extrapolations and uncovering hidden physical or causal interrelationships.
- Mathematical separation of steady trends, cyclic components, and noise in data series.
- Evaluation of growth functions for world population as a driver for broader correlations.
- Analysis of economic indices (Dow Jones) through time and population-dependent models.
- Examination of global temperature anomalies using separating functions to distinguish human-influenced trends from natural cycles.
- Critical assessment of the limits of extrapolation and the importance of model simplicity.
Auszug aus dem Buch
1 Selection of Meaningful Functions and Variables for the Analysis of Data Series
There are many types of time series, such as financial, demographical, economical, climatic, meteorological, environmental, measurements concerning atmospheric data and other types.
This paper deals specifically with the correlation of data on world population, long term measurements of world wide temperatures and also on long term changes of indices like the Dow Jones Industrial Index. These three time series serve as examples, but the findings can be applied generally.
Well known is the fact that some time series show a more or less perplexing inconsistency or anomaly, while others follow an astonishing regularity. Some of them seem to follow a long term trend superimposed by short term variations. Some others again seem to come and go like waves or other cyclic curves. Finally, some time series seem to be randomly distributed.
The purpose of this essay is to propose a method on how to separate long term steady trends from long term waves or random effects. What one needs first is a good, consistent, well-founded and reasonable function for the steady part.
Summary of Chapters
1 Selection of Meaningful Functions and Variables for the Analysis of Data Series: Introduces the methodology for identifying steady trends within complex time series by moving beyond simple time-based correlations.
2 Examples for Separating Functions: Details the mathematical approaches to model growth, cyclic components, and noise, providing the foundation for analyzing non-linear data structures.
3 Examples for the proposed Method: Applies the developed separation models to real-world datasets, specifically world population, the Dow Jones Industrial Index, and climate change temperature anomalies.
4 Conclusion: Summarizes the effectiveness of using mathematical correlations to explain complex systems and emphasizes the value of the philosophical "cause of the cause" approach in scientific modeling.
Keywords
Data Series, Correlation, Trend Analysis, Cyclic Components, World Population, Dow Jones Industrial Index, Climate Change, Mathematical Modeling, Extrapolation, Sigmoid Functions, Hyperbolic Growth, Data Noise, Time Series Analysis, Causality, Predictive Modeling
Frequently Asked Questions
What is the core focus of this research?
The research focuses on developing a mathematical framework to deconstruct complex data series into their constituent parts—steady trends, cyclic waves, and random noise—to better understand underlying drivers.
What are the central themes of the work?
The work centers on the interplay between time-based data and population-based growth models, applied specifically to financial markets, demographic trends, and climatic shifts.
What is the primary goal of the study?
The primary goal is to provide a robust method for creating meaningful, feasible extrapolations of data by replacing simplistic time-based variables with more relevant explanatory variables.
Which scientific methods are utilized?
The study employs non-linear optimization, multiple linear regression, and various growth functions (such as limited hyperbolic growth) to fit and separate data components.
What topics are covered in the main section?
The main section covers theoretical growth modeling, the application of these models to world population data, economic indices like the Dow Jones, and global sea/land surface temperature anomaly records.
How would you characterize this work based on its keywords?
The work is characterized as a rigorous quantitative study of time series, focusing on functional analysis and predictive modeling to distinguish genuine trends from noisy fluctuations.
How does the author treat the climate change data?
The author separates temperature anomaly data into a steady trend correlated with world population and a distinct natural cyclic component, demonstrating that short-term fluctuations can mask longer-term developments.
What is the significance of the "hiatus" discussed in the text?
The author argues that the observed climate "hiatus" is a result of natural cyclic downturns temporarily compensating for the underlying long-term steady trend, rather than a cessation of climate change.
Why is time considered a problematic variable by the author?
The author argues that time is merely a means of ordering observations; identifying time as the "cause" of a trend is often an error that fails to uncover the actual underlying physical or social drivers.
What does the author imply about future projections?
The author notes that all models are based on correlations rather than absolute physical laws, meaning they provide insights into the character of a model but should not be taken as absolute, immutable predictions.
- Arbeit zitieren
- Hans-Martin Stoenner (Autor:in), 2015, 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, München, GRIN Verlag, https://www.grin.com/document/301835
