Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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

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?

share|improve this question
up vote 3 down vote accepted

Use lagged temperatures with spline functions (not linear). There is a big literature on this. See, for example,

share|improve this answer
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).… – 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: – 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.

share|improve this answer
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

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.