example of monotonous nonlinear trend

Question

Can anyone give me a clear example of what a "monotonous nonlinear trend" is? I am trying to teach myself time series analysis and ran across this phrase. I know what a nonlinear trend looks like but what is a monotonous one? How does it differ from a non-monotonous nonlinear trend?

Answer 1

A monotone trend would be one that is either increasing, like this:

or decreasing, like this:

The trend below is not monotone.