A General Description of Growth Trends

TL;DR

This paper introduces a unified framework for describing growth deceleration in time series, providing a versatile tool for trend removal applicable to various domains like economics and epidemiology.

Contribution

It develops a general formalism for all growth functions with decreasing growth rates, extending previous models and enabling better trend analysis in diverse time series.

Findings

Deviations from exponential growth typically require only one or two parameters.

The framework effectively models growth deceleration in GDP, population, and pandemic data.

Potential for broad application in trend removal and time-series analysis.

Abstract

Time series that display periodicity can be described with a Fourier expansion. In a similar vein, a recently developed formalism enables description of growth patterns with the optimal number of parameters (Elitzur et al, 2020). 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 pure 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.