Question

Day	Demand Avg
Jan	88
Fab	89.06666667
Mar	88.375
Apr	88.03225806
May	86.53125
Jun	81.87096774
Jul	79
Aug	80.125
Sep	83.61290323
Oct	88.5
Nov	89.29032258
Dec	90.21052632

Estimate the January forecast using

1. Seasonal forecast.
2. 12-month moving average forecast.
3. Exponential smoothing (for an alpha of your choosing)
4. Calculate the Mean Forecast Error (MFE), Mean Absolute Deviation (MAD) and Mean Squared Error (MSE) and compare the results. Write a line or two explaining the superior model(s) for this particular data set including your reasoning.

Answer 1

Exponential smoothening with Alpha-0.5 12 month moving average Holt's Model edure Alpha (al) Arrange the data in tabular list format Using the formulas given below, calculate the forecast Month Demand 0.500 Fit) IError IErrorl Error Errorl2 0.500Eror IErrorl2 88.00 88.00 8.53 88.45 88.24 87.39 84.63 88.00 88.00 8.53 88.59 88.39 87.45 0.00 0.00 0.27 0.16 88.00 0.00 1.07 0.43 0.72 1.84 Exponential Forecast formula: Forecast for periodt- Forecast (t-1) Alpha (Sales(t-1)-Forecast t-1)) 89.067 88.375 88.0322 呂6.5312 81.8709 79 1.07 1.14 0.03 0.18 88.00 1.14 0.16 0.18 88.75 B8.37 86.97 82.67 78.16 76.96 9.77 85.80 90.08 Formula for Trend adjusted exponential simuothening 30.43 31.69 2.85 26.03 13.45 .B5 44.22 6.21 1.75 1.69 80.83 2.67 84 呂8.5 89.2903 90.2105 80.97 呂2.29 85.40 87.34 88.78 Formula for 12 period Moving average Average ( demand values from lan to Dec) Oct 6.21 38.55 15.17 8.22 80.29 0.52 8.73 2.B7 呂7.54 0.13 0.02 86.05 90.15 0.00 0.00 2.65 11.51 2.81 15.10 MSE MAD MSE MAD MSE MAD

To develop the seasonal forecast, Holt’s method of forecasting has been used.

The superior method will be one which has the least MAD and MSE value. We can see that 12 month MA does not qualify for this as most of the values are 0. The MAD and MSE of Exponential smoothening is lesser than the Holt’s method. So, we can say that Exponential method is more superior forecasting method in this case as the deviation from actual values is lesser.