Gompertz: Each time series is modeled using a Gompertz curve. These curves take the shape of an S and come with lower and upper bounds on the curve.
Equation:
Yt = 10 a - b(rt)
where, a, b and r are positive constants, r is less than 1 and t=1 for year 1.
We coluld rewrite it as:
Log Yt = a - b(rt)
The it is similar as the modified-exponential form.
For the Gompertz, the logaritm of the ratio of the slope to the moving average when plotted against time gives a straight line sloping down to the right, which is the slope characteristic.
We can imagine that there are two straight lines in the slopes chart. From 2007 to 2011 and the other from 2011 to 2019. It is difficult to be sure that there is a trend with too little data . If we are confident that there is a parabolic trend - say from 2010 to 2021 -, then we can calculate it with the application.
There some differences between the equation and the table data due to rounding effects.
One that the application suggest is shown in next graph.
Equation where Y is the parabolic trend line.
Yt = -0.24t2 + 7.98t + 18.67
The parabolic curve type is useful for data that changes direction over time, either increasing then decreasing or vice versa. All other curve types assume that the values continuously increase or decrease over time.
Equation where Y is the parabolic trend line with moving averages.
Yt = -0.27t2 + 8.18t + 18.55