On the adequacy of the polynomial approximation to the exponential growth curve model

Abstract

Exponential growth curves are usually approximated with a finite order polynomial curve in the study of trending curves. This is done because the most popular way of removing the trend component is by differencing. This paper shows that the trend curve cannot be removed by differencing when the trend curve is the exponential growth curve. Exponential curves are transcendental functions which can be reduced to a finite order polynomial by Maclaurin series expansion. The objective of this paper is to examine the adequacy of the polynomial approximation of the exponential growth curve with respect to its growth rate and sample size. The coefficients of the associated polynomial curve were obtained theoretically by the use of Maclaurin series expansion method. Next, exponential growth curves with varying growth rates and sample sizes were simulated. Adequate polynomials were fitted to the simulated exponential growth curves and the coefficients obtained were compared with the theoretical coefficients using absolute error and paired tests. Results obtained show that adequacy depend on both growth rate and sample size. For the purpose of statistical analysis, the highest sample size of 28 is not useful, especially in times series analysis where the demand of samples of 60 or more is made.