A General Description of Growth Trends

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.

Keywords

• exponential growth
• logistic growth
• growth hindering
• time series analysis
• trend removal