A note on the turning point for the quadratic trend

Abstract

The quadratic trend is a statistical model described by the quadratic function. Finding its extremum (also called the vertex or the turning point) using differential calculus or completing the square method is very well known in the literature. In this paper, a new method for finding the extremum of the quadratic function, based on a simple mathematical inequality is proposed. In comparison with the other two known methods, our method does not require the differentiability assumption and it takes fewer steps than completing the square method. Also, it is shown how the turning point for the quadratic trend can be applied in forecasting the unemployment rate in Croatia in the first quarter of 2019. The obtained conclusions are equal to the conclusions obtained in the usual way by using forecasting software.