Question

3. A car dealer must choose between two alternative forecasting techniques. Both techniques have been used to prepare forecasts for a six- month period. Using MAD as a criterion, which technique provides a more accurate forecast? Using MSE as a criterion, which technique provides a more accurate forecast? Month Demand Technique 1 Forecast Technique 2 Forecast 1 492 488 495 2 470 484 482 3 485 480 478 4 493 490 488 5 498 497 492 6 492 493 493

Answer 1

From both criterion, MAD and MSE, technique 1 is more accurate forecast than technique 2 forecast.

Step-by-step explanation:

First of all let's sort out this data:

Month . Demand . Technique 1 Forecast . Technique 2 Forecast

1 492 488 495

2 470 484 482

3 485 480 478

4 493 490 488

5 498 497 492

6 492 493 493

Now, first part is to check the accuracy of the forecast using MAD.

Where,

MAD = Mean Absolute Deviation.

Formula = (Sum of all absolute differences between demand and forecast)/ Time period

And the rule is, we will compare final MAD values of both the techniques and compare. The lower value will be considered as accurate forecast technique.

So, for Technique 1, we have:

Month . Demand(D). Technique 1 Forecast(F) |D-F|

1 492 488 4

2 470 484 -14

3 485 480 5

4 493 490 3

5 498 497 1

6 492 493 -1

(neglecting negative sign because of absolute) Total = 28

MAD = Total SUM / Time period

Time Period = 6

MAD = 28/6

MAD = 4.66

Now, let's do it for Technique 2:

Month . Demand . Technique 2 Forecast . |D-F|

1 492 495 -3

2 470 482 -12

3 485 478 7

4 493 488 5

5 498 492 6

6 492 493 -1

(neglecting negative sign because of absolute) Total = 34

MAD = Total SUM / Time period

Time Period = 6

MAD = 34/6

MAD = 5.66

Hence, Technique 1 is accurate forecast using MAD because it has lower MAD value.

Now, the second part of the question is to solve this by using MSE.

And the rule is, we will compare final MSE values of both the techniques and compare. The lower value will be considered as accurate forecast technique.

MSE = Mean Squared Error

Formula = (Sum of all squared differences between demand and forecast) /Time period

Let's do it for Technique 1:

Month . Demand(D). Technique 1 Forecast(F) (D-F) . (D-F)²

1 492 488 4 16

2 470 484 -14 . 196

3 485 480 5 . 25

4 493 490 3 9

5 498 497 1 1

6 492 493 -1 1

(Add all (D-F)² values for the total) Total = 248

MSE = Sum Total/ Time period

MSE = 248/6

MSE = 41.33

Similarly for Technique 2:

Month . Demand(D). Technique 2 Forecast(F) (D-F) . (D-F)²

1 492 495 -3 9

2 470 482 -12 . 144

3 485 478 7 . 49

4 493 488 5 25

5 498 492 6 36

6 492 493 -1 1

(Add all (D-F)² values for the total) Total = 264

MSE = Sum Total/ Time period

MSE = 264/6

MSE = 44

According to MSE as well, technique 1 forecast is accurate because it also has lower value than technique 2.