Question

Using the SES method, find the Forecast, Error and Bias.
Week1: Demand=1, Forecast=? Error=?
Week2: Demand=13, Forecast=? Error=?
Week3: Demand=4, Forecast=? Error=?
Week4: Demand=15, Forecast=? Error=?
Week5: Demand=14, Forecast=? Error=?
Week6: Demand=18, Forecast=? Error=?
Week7: Demand=20, Forecast=? Error=?

Answer 1

I can do this, but I need one assumption: the smoothing constant α and the initial forecast F1. A common choice is α = 0.3 and set the initial forecast F1 = D1 (so F1 = 1). Using Simple Exponential Smoothing with those choices:

Formula: Ft = Ft-1 + α(Dt-1 − Ft-1) (forecast for period t is updated after observing period t−1).

Using α = 0.3 and F1 = 1:

Week 1: Demand = 1
- Forecast F1 = 1
- Error e1 = D1 − F1 = 0.00

Week 2: Demand = 13
- Forecast F2 = 1.00
- Error e2 = 13 − 1 = 12.00

Week 3: Demand = 4
- Forecast F3 = 4.60
- Error e3 = 4 − 4.60 = −0.60

Week 4: Demand = 15
- Forecast F4 = 4.42
- Error e4 = 15 − 4.42 = 10.58

Week 5: Demand = 14
- Forecast F5 = 7.59
- Error e5 = 14 − 7.59 = 6.41

Week 6: Demand = 18
- Forecast F6 = 9.52
- Error e6 = 18 − 9.52 = 8.48

Week 7: Demand = 20
- Forecast F7 = 12.06
- Error e7 = 20 − 12.06 = 7.94

Bias (mean error) = (sum of errors)/7 = (0 + 12 − 0.6 + 10.58 + 6.406 + 8.4842 + 7.93894) / 7 ≈ 6.40

If you want a different α or a different initialization for F1 (e.g., an average or an external prior), tell me the value and I’ll recompute.