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Consider the following time series: Period 1 2 3 Demand 15 24 26 Forecast the demand for period 3 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 3 using exponential smoothing with W (smoothing coefficient) = 0.4. Express your answer without rounding

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Solution

To forecast the demand for period 3 using exponential smoothing, we first need to understand the formula for exponential smoothing:

Ft = Ft-1 + W(Dt-1 - Ft-1)

Where: Ft = Forecast for the upcoming period Ft-1 = Forecast of the previous period W = Smoothing coefficient (given as 0.4) Dt-1 = Demand of the previous period

Given that we don't have a forecast for period 1, we'll use the demand of period 1 (15) as the forecast for period 1.

Now, let's calculate the forecast for period 2:

F2 = F1 + W(D1 - F1) F2 = 15 + 0.4(15 - 15) F2 = 15

Now, we can calculate the forecast for period 3:

F3 = F2 + W(D2 - F2) F3 = 15 + 0.4(24 - 15) F3 = 15 + 0.4(9) F3 = 15 + 3.6 F3 = 18.6

So, the forecast for period 3 using exponential smoothing with a smoothing coefficient of 0.4 is 18.6.

This problem has been solved

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