# How to calculate confidence interval for difference (or ratio) of two different time series?

I have two time series which are sampled at the exact same times. I would like to calculate a confidence interval either for the ratio between the two or the difference between the two. The values tend to be somewhat similar, but both have a large amount of what looks like random noise superimposed on them (much larger than the potential difference, at any particular point in time). What is the appropriate method to calculate a confidence interval in this case?

P.S. The data is very different from being normal; it is roughly flat-top, pretty similar shape (but perhaps shifted) for the two series.

• Why not compute the ratio, or the difference, and model that time series, forming whatever kind of interval you need, as you would for a univariate series. – Glen_b -Reinstate Monica Aug 14 '14 at 23:04
• @Glen_b: Thanks! Does that lose any statistical power? Also, how do I form an interval for a univariate series? – Alex I Aug 14 '14 at 23:31
• I can't really respond without being more clear about the circumstances. For example, knowing what, exactly you're forming an interval for. If it's a CI, you're presumably forming an interval for some population quantity (like a mean) ... but what quantity? – Glen_b -Reinstate Monica Aug 14 '14 at 23:35