What problems should I watch out for when combining multiple time series? Say I have a number of time series, e.g. a number of temperature records from various stations in a region. I want to get a single temperature record for the whole region with which I could describe aspects of the regional climate. The intuitive approach might be to simply take the average of all stations at each timestep, but my statistical spider-sense (which I'm definitely not well in touch with yet) tells me that this might not be so easy. In particular, I imagine that averaging over the entire region will remove some of the interesting temperature extremes, and I might have problems with dependence between close stations.
What other problems might I face if I tried a strategy like this, and are there ways to overcome them, or more sensible methods of combining this kind of data?
Note: Answers can be more general than the spatial example I've provided.
 A: First, I'd like to say that I would be adding a comment, but I can't do that yet (rep), but I like the question and wanted to participate, so here's an "answer".  Also, I see that this is old, but it's interesting.
First, would it be possible to use a dimension-reduction technique, like PCA, to condense the time series?  If the first eigenvalue is large, maybe that means that your use of the eigenvector would represent most of the dynamics.
Second, and more generally, what is your desired use of the time series?  Not knowing much else, I would guess that the temperatures could vary quite a bit.  E.g., if some temperature records are near cities, you could get a "heat island" type effect.  Or perhaps a small change in lateral distance happens to yield a large change in vertical distance--- one location could be at sea level and right on the ocean, and another not "too far away", but at a kilometer in elevation.  Those would definitely have different temperatures!
These are just some thoughts.  Maybe someone else could jump in and give a better answer.
