With a smoothing constant of α = .2, the equation below shows that the forecast for week 13 of the gasoline sales data from Table 17.1 is given by F13 = .2Y12 + .8F12. However, the forecast for week 12 is given by F12 = .2Y11 + .8F11. Thus, we could combine these two results to show that the forecast for week 13 can be written: F13 = .2Y12 + .8(.2Y11 + .8F11) = .2Y12 + .16Y11 + .64F11 Exponential Smoothing Forecast Ft+1 = αYt + (1 α)Ft where Ft+1 = forecast of the time series for period t + 1 Yt = actual value of the time series in period t Ft = forecast of the time series for period t α = smoothing constant (0 ≤α≤ 1) Gasoline Sales Time Series Week 1 2 3 4 5 6 7 8 9 10 11 12 Sales (1000s of gallons) 17 21 19 23 18 16 20 18 22 20 15 22 a)Making use of the fact that F11 = .2Y10 + .8F10 (and similarly for F10 and F9), continue to expand the expression for F13 until it is written in terms of the past data values Y12, Y11, Y10, Y9, Y8, and the forecast for period 8. b)Refer to the coefficients or weights for the past values Y12, Y11, Y10, Y9, Y8. What observation can you make about how exponential smoothing weights past data value in arriving at new forecasts? Compare this weighting pattern with the weigh
With a smoothing constant of α = .2, the equation below shows that the forecast for week 13 of the gasoline sales data from Table 17.1 is given by F13 = .2Y12 + .8F12. However, the forecast for week 12 is given by F12 = .2Y11 + .8F11. Thus, we could combine these two results to show that the forecast for week 13 can be written: F13 = .2Y12 + .8(.2Y11 + .8F11) = .2Y12 + .16Y11 + .64F11
Exponential Smoothing Forecast Ft+1 = αYt + (1 α)Ft where Ft+1 = forecast of the time series for period t + 1
Yt = actual value of the time series in period t
Ft = forecast of the time series for period t α = smoothing constant (0 ≤α≤ 1)
Gasoline Sales Time Series
Week 1 2 3 4 5 6 7 8 9 10 11 12
Sales (1000s of gallons) 17 21 19 23 18 16 20 18 22 20 15 22
a)Making use of the fact that F11 = .2Y10 + .8F10 (and similarly for F10 and F9), continue to expand the expression for F13 until it is written in terms of the past data values Y12, Y11, Y10, Y9, Y8, and the forecast for period 8.
b)Refer to the coefficients or weights for the past values Y12, Y11, Y10, Y9, Y8. What observation can you make about how exponential smoothing weights past data value in arriving at new forecasts? Compare this weighting pattern with the weighting pattern of the moving averages method.
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