Consider the following time series: Period 1 2 3 Demand 15 24 26 Forecast the demand for period 4 using exponential smoothing with W (smoothing coefficient) = 0.4. Express your answer without rounding.
Question
Consider the following time series: Period 1 2 3 Demand 15 24 26 Forecast the demand for period 4 using exponential smoothing with W (smoothing coefficient) = 0.4. Express your answer without rounding.
Solution
To forecast the demand for period 4 using exponential smoothing, we first need to understand the formula for exponential smoothing:
Ft+1 = W*Dt + (1-W)*Ft
Where: Ft+1 = Forecast for next period W = Smoothing coefficient Dt = Demand in current period Ft = Forecast for current period
Given that W = 0.4, and we have the demand for periods 1, 2, and 3, we can start by assuming the forecast for period 1 (F1) is equal to the demand in period 1 (D1). So, F1 = 15.
Next, we calculate the forecast for period 2 (F2) using the formula:
F2 = W*D1 + (1-W)F1 F2 = 0.415 + (1-0.4)*15 = 15
Then, we calculate the forecast for period 3 (F3):
F3 = W*D2 + (1-W)F2 F3 = 0.424 + (1-0.4)*15 = 18.6
Finally, we calculate the forecast for period 4 (F4):
F4 = W*D3 + (1-W)F3 F4 = 0.426 + (1-0.4)*18.6 = 21.96
So, the forecasted demand for period 4 using exponential smoothing with W = 0.4 is 21.96.
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