Another example

(if you come across this post by accident -- this post is about a time series that I am not at liberty to discuss freely. You may want to click on the category link to get a feel for what is happening)

Below are the two main series. There is one very obvious outlier at period 200.

 

I've computed the ratio of one series over the other (R/S). I've also fitted a robust estimate of a non-linear trend of the form y = a + b(T^delta/(T+gamma)). A robust estimator is probably better in this case because there are several outliers (9 obvious instances). There is also a noticeable wave pattern occurring between periods 145-209.

The third graph shows the reciprocal series (S/R).