Consider the following time series: Period 1 2 3 4 5 6 7 8 Demand 15 24 26 33 20 22 27 20 Calculate the exponentially smoothed value for period 2 using W (smoothing coefficient) = 0.4. Express your answer without rounding.
Question
Consider the following time series: Period 1 2 3 4 5 6 7 8 Demand 15 24 26 33 20 22 27 20 Calculate the exponentially smoothed value for period 2 using W (smoothing coefficient) = 0.4. Express your answer without rounding.
Solution 1
To calculate the exponentially smoothed value for period 2, we use the formula:
S_t = α * D_t-1 + (1 - α) * S_t-1
where:
- S_t is the smoothed value for the current period
- D_t-1 is the demand in the previous period
- S_t-1 is the smoothed value for the previous period
- α is the smoothing coefficient
Given that α = 0.4, D_1 = 15 (demand in period 1), and S_1 = D_1 = 15 (since the smoothed value for the first period is usually set to the demand in the first period), we can substitute these values into the formula to find S_2:
S_2 = 0.4 * 15 + (1 - 0.4) * 15 S_2 = 6 + 9 S_2 = 15
So, the exponentially smoothed value for period 2 is 15.
Solution 2
To calculate the exponentially smoothed value for period 2, we use the formula:
S_t = α * D_t-1 + (1 - α) * S_t-1
where:
- S_t is the smoothed value for the current period
- α is the smoothing coefficient (W)
- D_t-1 is the demand in the previous period
- S_t-1 is the smoothed value for the previous period
Given that α (W) = 0.4, D_1 = 15 (demand in period 1), and S_1 = D_1 = 15 (since the smoothed value for the first period is usually set to the demand in the first period), we can substitute these values into the formula to find S_2:
S_2 = 0.4 * 15 + (1 - 0.4) * 15 S_2 = 6 + 9 S_2 = 15
So, the exponentially smoothed value for period 2 is 15.
Similar Questions
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