# 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.

• The problem might be in your conflict between "a single temperature record for the whole region" and any interest you have in intra-region variation. A solution might involve some way of reconciling these two issues eg partitioning variance into intra- and inter- region components. Apr 5 '12 at 10:38
• @PeterEllis, yeah, I was vaguely thinking of that. For the purposes of the question, let's assume I don't care about intraregional spatial variability. Apr 5 '12 at 10:56
• in that case, I think the main thing you have to worry about is the dependence between close stations. Find a way to weight down observations that effectively duplicate the station next door, and you should be ok. Apr 5 '12 at 11:16
• @PeterEllis: ok, but there might not be a reasonable physical way to do that - Closeness of stations doesn't necessarily mean that they are more dependent - ie. two close stations on the opposite sides of a mountain range might be less similar than two distant stations on a broad plain. Is there a reliable way to define dependence statistically? Covariance, I suppose... There are still likely to be less peaks in the resultant series (I guess that reflects the physical situation though - temp changes over a broad region are likely to be slower and steadier than at a single place). Apr 5 '12 at 11:31
• @naught, regarding the spatial aspect of your question, how are your regions defined? In your comment, you mention that two close stations on opposite sides of a mountain could be different from two distant stations on a broad plain. Have you considered re-defining the station regions based upon proximity and similarity for your analysis? They wouldn't have to necessarily match up to conventional regional boundaries. Instead they could become an analytical overlay that could be plotted over a traditional map.
– dav
Apr 5 '12 at 11:43