What is the best model for this data?
"Best" depends on the task. I think your task is one of the examples below.
The data is continuos. The neighbor is the similar value.
And long term range is wider than short term range.
So easy prediction is that to use the value of the neighbor.
The next idea is using the peridiocity.
Without considering periodicity, The data has two terms, constant and increasing.
If we think the increasing does not stop, we can make the model. Single regression using only the incrasing term data is the easiest model.
Conbination with ReLU function may be good.