Part 2. MM4XL Tools > 1. Strategic Tools > Forecast Manager > 2. Anatomy of a Forecast Manager Output Report > 4. Control charts

Forecast Manager

4. Control charts

Forecast Manager prints three different charts:

  • Forecast chart
  • Cumulative sum control chart (CuSum)
  • Special events chart

The Forecast chart shows how well the best curve fits the actual data. You can see the forecasted values and, if you chose to do so, the confidence interval above and below fitted values can be shown on chart, also the accuracy coefficients are shown in form of legend. This chart (see example below) is useful during presentations, for taking a quick look to the best fit. However, it does not supply much information about how well the model worked, although all fit coefficients as well as both Theils U (goodness of fit) and Durbin-Watson coefficient (autocorrelation of error terms) are available.

Sales Forecast Software with Sales History Data

The Cumulative Sum chart, often called CuSum chart, is used for diagnosing the functioning of forecasting models. The whole concept is based on the fact that forecasting errors must be randomly generated as long as the model predicts correctly, which is not accurately. Random terms show a normal distribution with average equal to zero and standard deviation equal to

Sales Forecast Software with Sales History Data
. In case of systematic errors the blue line (cumulative error) in the chart below would trespass one of the red boundaries, and this would be the signal of an incorrect functioning of the model, which suggests for adjusting the model parameters. The boundaries are typically set at 2 standard deviations of the cumulative error term above and below the zero line, which is also the default value Forecast Manager uses. Read Lewandowski (pg 155) for references to this topic.

Sales Forecast Software with Sales History Data

We called the last chart Special Events chart, and it works pretty much like the CuSum chart above. The difference is that it works with the error term not cumulated and the chart is used for highlighting periods that exhibit an abnormal error size, either larger or smaller that expected. The expected boundaries are set by means of standard deviation computed on the error terms. Read Bail and Peppers (pg 131) for references to this topic.

Forecast errors lying outside two standard deviations are identified as abnormal and are highlighted with either a red (lost) or green (won) marker. The forecasted amount above or below the limit is then computed and displayed in a label in original units and percentage.

Sales Forecast Software with Sales History Data

In the chart above there are two abnormal quantities. The one at time 7 is of positive nature, and it brought 2.4 units, or 0.9%, more sales than expected. If we were running a promotional action this might have been the result of that action. On the other side, the red marker highlights a lost larger than expected in time 19. The legend in the upper right corner of the chart summarizes all favorable and adverse events.

Abnormal quantities measured at the beginning of the time series, as in our example, can be attributed to the adapting effect of the algorithm to the actual values. Therefore, we suggest, when possible, to use time series that do not exhibit such movements at the beginning of the series.

Finally, there is another graphical control chart worth mentioning here, although it is not implemented in MM4XL. We are talking of the Turning-Point diagram. A turning-point happens when the slope of the actual curve changes direction. The table Reliability & Accuracy Measures reports about turning-point performance. The series Appliance Shipment we used in our example, for instance, exhibits 10 turning-points, and the model did not match 6 of them (Missed signals). On the other side the model predicted 12 times a change in direction, which actually did not happen (False signals).

Turning-points are often more important to managers than the trend itself. Indeed, forecasting accurately when a change in slope is going to happen may help saving or making more money. There are four basic turning possibilities, as arranged in the table below:





No Turning-point






The number of False Signals is found with:

Sales Forecast Software with Sales History Data

The number of Missing Signals is found with:

Sales Forecast Software with Sales History Data

Turning-point performance in the Reliability Measure table starts counting fitted values from the third value plus the number of moving periods on. A condition required by some models we coded.

An example of Turning-Point Diagram is shown below together with a legend picture that shows the meaning attributed to each portion of the diagram. The coordinates needed for plotting the points on the chart can be found with the formula:

Predicted (horizontal axis):

Sales Forecast Software with Sales History Data

Actual (vertical axis):

Sales Forecast Software with Sales History Data

Sales Forecast Software with Sales History Data

Panel I and IV above host the 12 false signals mentioned above and reported in the Reliability & Accuracy Measures table. Read Bail and Peppers for references to this topic.

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