Click on  above “Selections” and click again on  at the bottom left of the dialog box displayed. Select “Automatic”. This changes the behaviour for the grid at the top. You can select the cells instead of typing numbers in the cells. If a cell is selected, this means for the current forecast horizon that the corresponding selected forecast must be included as an explanatory variable in the regression. Two regressions will be calculated in the example below; one for the interval 13-24 hours, and one for 25-36 hours ahead. Both of these will include forecasts from the suppliers “Weather 1”, “Weather 2” and “Weather 3” as explanatory variables. The program will automatically enter weights for the forecast horizons not selected so that the calculated weights for row 3 will be copied to rows 1 and 2. Likewise, if this weighting is to be evaluated for more than 36 hours ahead, the “25-36” hour weighting will be used. These calculations are time-consuming, and there may be a need to limit the number of regressions to the forecast horizons for which you are most in need of minimising balance errors.

When you change the weighting from “Manual” to “Automatic”, a range of options will be displayed in the dialog box. The step-wise regression allows you to remove weather forecasts which do not make a sufficient contribution to the explanation of the outcome. As a first step, the step-wise regression algorithm used identifies the forecast which alone can explain as much as possible of the variation of the historical outcome. After this forecast is included,  a search is carried out for the remaining forecasts which one alone can describe most of the remaining variation.

In a third step, a search is carried out for the remaining forecast which best explains what now remains of the outcome to be explained, and so on.

After a number of steps, the inclusion of a new forecast will only marginally improve the results, and this improvement can be purely randomly induced by conditions during the evaluation period.

The stopping criteria for the step-wise parameter selection procedure are 2 significance test (F-tests). There is a certain degree of uncertainty with every statistical test, and we have decide what risk we are prepared to accept in the significance test.

In the “Regression” box, you can enter:

•      F-value include:  Enter the risk you are prepared to take of including a new variable totally uncorrelated with the historical outcome. If you want it not to accept errors more frequently than in 5% of cases, enter 0.05 under the header “F-value include”.

•      F-value exclude: The step-wise  algorithm also has the option to throw out a variable which was important in an earlier step but which is no longer important when another one or more variables have been added. The risk you want to take of not throwing out a previously totally uncorrelated variable with the historical outcome is specified under the header:  “F-value exclude”. A value higher than “F-value include” will give a conservative model which generally does not throw out variables which have already been included.

•      Trim fraction: The exact proportion of extreme values that are to be excluded from the regression. The entire interval between the forecast minimum value of the evaluation period and its maximum value is divided up into a number of sub-intervals. For each sub-interval the highest and lowest measured values are removed from the regression. A high value gives regression results towards a minimization of the mean absolute error (MAE), in contrast to an ordinary regression (value 0) that minimises RMSE.

•      Normalize weights: The result of a regression normally gives a total of the weights which differs from 100% and a constant non-zero term. This may be justified as forecasts for a specific forecast horizon may systematically deviate from the observed weather on which the forecast models are trained. If, instead, you want the result to reflect a “trust” you have for the various weather forecasts, you can check this check box. The total of the weights can then be scaled up to 100% and the constant is omitted.

•      Allow negative weights: The linear regression can also result in negative weights. Uncheck this if these are not to be permitted.

The “Tolerance” box contains options for defining settings for warning messages from the regression process. Normally, the results from regression should give positive weights (possibly also a slight negative) which are close to 1 when totalled. The constant should also be small in relation to the mean load. Deviations from this may indicate problems somewhere in the forecast processes.

•      Max sum of abs weights: If you allow negative weights, the absolute sum of individual weights may be significantly higher than 100% even if the total of weights is close to 100%. For example, a regression may set 200% weight on forecast 1 and -100% on forecast 2. Set the highest accepted total of the absolute sums of the weights.

•      Min sum of weights: The program issues a warning if the sum of weights falls below this value.

•      Max constant absolute value: The program issues a warning if the absolute value of the constant estimated during regression exceeds the specified percentage (percentage of the mean load during the evaluation period).

When we are satisfied with our settings, these are saved as a “Selection” which then can evaluate. During evaluation, you will first calculate the optimal weights for all forecast series for all series you selected. In step two, these will then be evaluated for the forecast horizons entered in an “extract”.