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Well, your model matches the observations quite nicely. That actually would raise red flags for me if they lined up that well (accidentally plotting the same data twice, for example).
Personally, I would never offset my plots like you are asking for. It is misleading and can lead to confusion. Instead, I would plot the first line thicker than the second one. But, if you really want to do the offset, you can just add a constant to the x values when calling plot() for the second one.
Since this isn't a bug report, I am going to go ahead a close this. Typically, these sorts of questions are dealt with on the mailing list or stack overflow.
As an additional note, if you look carefully, that example plot isn't actually offset. All pairs of markers have the same x coordinates. So the interpretation of that graph should be that the model is offset delayed.
I have original data and prediction data and when I draw them they overlap
this is the plot:
I want to make spaces between the two lines like the following plot:
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