1. 1 Forecasting

2. 2 Should you carry an umbrella today? Part of the answer for you most likely depends on how much you care about getting wet! Assuming you care, then you have to look to the future and think about what you think might happen. You would be making a forecast, even if you have listened to the weather report. In a business setting we often can use a forecast as well. We might like to forecast sales, profit, the consumer price index, or units sold by a competitor. We have already seen how regression analysis can be used to forecast. In a few slides we will turn to other methods, but first let’s look at how to evaluate the accuracy of forecasts.

3. 3 MAD – Mean absolute deviation In general, the forecast error or deviation is defined as the actual value minus the forecast value. Say di is the deviation for the ith unit, where units can be time periods or objects, and say xi is the actual value and fi is the forecast value. Then di = xi – fi. In a data set when we have values for the actual data and forecasts, MAD = Σ׀di ׀ / n, or in words you take the absolute value of all the deviations, then add up the absolute values and then divide the sum by the number of values added. A method of forecasting is called better if the method has a lower MAD.

4. 4 Example of naïve model – make forecast for next period by using this period’s value as next period’s forecast Yearactual valueForecastdeviation 1110xxxxxxxx 2100110-10 3120100 20 4140120 20 5170140 30 You will notice we have 5 years of actual data. Since we have a naïve model we can make 4 forecasts. MAD = (10+20+20+30)/4 = 20

5. 5 Moving average To forecast using the moving average method you take the most recent n values to forecast the value for the next period. n stands for the amount of the moving average. If n = 3 we have a three month moving average. On the next slide let’s evaluate the three month moving average method for the data we had before. Note we will not able to have a forecast until the 4 th period.

6. 6 Example of 3 period moving average – make forecast for next period by using the most 3 recent data values. Yearactual valueForecastdeviation 1110xxxxxxxx 2100xxxxxxxx 3120xxxxxxxx 4140110 30 5170120 50 You will notice we have 5 years of actual data. Since we have a 3 period moving average model we can make 2 forecasts. MAD = (30+50)/2 = 40

7. 7 Note in the 3 period moving average example that the first forecast we is (110 + 100 + 120)/3 = 110. This can be rewritten as (1/3)110 + (1/3)100 + (1/3)120. So in the 3 period moving average each data point is weighted the same, with 1/3 as the weight for each points (the weight is 1/n in general). A weighted 3 period moving average would use each of the three data points, but would use different weights. Maybe you would want to weight more recent values higher than other values. The weights would still have to add to 1.

8. 8 Exponential Smoothing In the context of this method let’s call the current period the period for which we want the forecast and then last period is the period before the current period. The current period forecast is thus Last period’s forecast plus a fraction of (last period’s actual value minus last period’s forecast). Note, here we can not really forecast until the second period. But we have to have a forecast from the first period – seems contradictory. We will assume a forecast for the first period was the actual value. Continuing our example….

9. 9 Example of exponential smoothing with the fraction being =.1 Yearactual valueForecastdeviation 1110110 0 2100110-10 3120109 11 4140110.1 29.9 5170113.0956.91 MAD = (0+10+11+29.9+56.91)/4 = 26.9525 Note that since we didn’t really forecast period 1 we do not use that period in the MAD.

10. 10 In QM for Windows we can do this forecasting work. Go to the forecasting module Go to file new time series analysis The number of past periods should be the number of data points you have. When you hit ok here you see the input screen. Input the data (QM for windows has the word demand, but we can have other data.) The method “Naïve” is the default method. If you change method to moving average you have to also include the value for n. If you change the method to exponential smoothing you have to pick the fraction value.

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12. 12 The output screen “details and error analysis” is useful. You see the MAD for the model. SO, we have introduced some methods of forecasting here and the choice of method can be picked by the one with the lowest MAD.