# Load forecast model with temperature data

I would like to estimate a regression model of the type:

$load_t = seasonality_t + trend_t + \beta * temperature_t,$

and I have load data and temperature on high frequency (hourly data). My impression is that the temperature does not influence load at the same frequency as I measure load (i.e. a change in temperature for 2 or 3 hours does not imply a change in load immediately). This is how I understand the application of the concept of coherency as in http://eprints.nuim.ie/1968/1/JR_C81dfisf.pdf

I tried to look at average temperature per day and use this in the regression but the results were not satisfying. How can we incorporate temperature into a practical model in the best way? Any hints? Good references?

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Use lagged temperatures with spline functions (not linear). There is a big literature on this. See, for example, http://robjhyndman.com/papers/stlf/

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Once again, thanks for your help, Rob. –  Richard Jan 14 '13 at 9:45
I am not familiar with the concept of regression splines - do you have any good reference at hand? Thank you! –  Richard Jan 16 '13 at 17:13
Try Ruppert, Wand and Carroll (2003). amazon.com/… –  Rob Hyndman Jan 17 '13 at 0:08
To other readers of the post, there is an R package and the following intro by Wand for the topic: uow.edu.au/~mwand/SPmanu.pdf –  Richard Jan 18 '13 at 8:42
Wand himself also pointed me to the package mgcv –  Richard Feb 1 '13 at 11:50

Here's an example of a monthly load model that clearly shows the role of temperature.

http://revgr.com/2012/11/06/all-forecasts-are-wrong-but-some-generate-fewer-complaints/

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Thanks - this is a nice post! Maybe not directly applicable to my intraday setting, but very illustrative. –  Richard Feb 1 '13 at 15:50
@Richard - I don't know the details of your particular problem, but is it possible that using monthly data to estimate the temperature coefficients is a worthwhile first step? Using those coefficients, can't temperature be "removed" from the intraday data so that what's left is the hourly "population/activity" term? –  bill_080 Feb 1 '13 at 16:35
At the moment I don't have enough data history (it is data per customer) that's my problem. But thanks again your input is definitely useful. –  Richard Feb 1 '13 at 17:41