Abstract
Time series that display periodicity can be described with a Fourier expansion. In a similar vein, a recently developed formalism enables the description of growth patterns with the optimal number of parameters. The method has been applied to the growth of national GDP, population and the COVID-19 pandemic; in all cases, the deviations of long-term growth patterns from purely exponential required no more than two additional parameters, mostly only one. Here, I utilize the new framework to develop a unified formulation for all functions that describe growth deceleration, wherein the growth rate decreases with time. The result offers the prospects for a new general tool for trend removal in time-series analysis.
Highlights
Positive Z indicates an increasing trend; for example, Z = 3 is a 3σ evidence for a growth trend. This non-parametric test can detect a monotonic trend in the time series of at least eight members [14] without assuming the data to be distributed according to any specific rule
The model finds that the hindered domain was entered in 1914, and predicts a 2050 population of 400 million, growing at 0.65% per year
We developed here a unified scheme for all patterns of decelerated growth (Section 3.1)
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Exponential trends can be handled by switching to the logarithm of the data points, transforming the time series into one with a linear trend that is removed by differencing Effective, this technique is only applicable to growth at a constant rate. In contrast with the handling of periodic variations, where Fourier analysis provides the foundation for a universal technique, a general method for the removal of monotonic long-term trends from time series is not yet available. The prospects for such a framework exist thanks to the newly developed hindering formalism to extract the exponential component from a growth process and describe the remainder with the optimal number of parameters [6].
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