Averaging the Weather First or Averaging the Energy Forecast

There is a question that has long vexed me: If we calculate a normal series of weather variables by averaging them first and running them through a model, do we get the same energy forecast if we run each year’s weather variables through the model and average the energy forecasts?

To answer this question, I did the following:

1. Calculated ‘normal’ weather as an average for the years 2010, 2011, 2012 and 2013 for both Cooling Degree Days (CDD) and Heating Degree Days (HDD) variables. Clearly, nobody should use four years as the basis for calculating normal weather. The point of this is to calculate a ‘normal’ series over a manageable number of years for illustrative purposes.
2. Built a simple monthly residential average-use model, which includes four variables:
   • Trend Variable: A simple linear trend variable
   • CDD65: Cycle-weighted CDD with a base of 65 degrees, which contains actual values during history and ‘normal’ during the forecast period
   • HDD55: Cycle-weighted HDD with a base of 55 degrees, which contains actual values during history and ‘normal’ during the forecast period
   • BDays: Billing days per month
3. Executed the forecast model with the ‘normal’ CDD65 and HDD55 variables with the following weights for each year under the following five scenarios:

In other words, the AvgScenario calculated the normal January as the average of the Januarys in 2010, 2011, 2012 and 2013. The same is true for the normal December, which is calculated as the average of the December values in 2010, 2011, 2012 and 2013.

The 2010Scenario calculated the normal as simply the 2010 values. That is, January will always be the January 2010 value and December will always be the December 2010 value.

And so forth.

I then extracted the forecast values from each of the five scenarios and compared the AvgScenario to the average of the other four scenarios.

The following compares the predicted values from the AvgScenario (which contains the average weather data) with the 2010 scenario (which contains the 2010 weather), along with the 2011, 2012 and 2013 scenarios. The final column, labeled AvgOfScenario is the average of 2010Scenario, 2011Scenario, 2012Scenario and 2013Scenario.

The takeaway is that the two highlighted columns (AvgScenario and AvgOfScenarios) display identical values. The answer to our original question is: Yes, we do in fact obtain the same results if we average the weather first or if we run each year through the model and average the results.