the forecast for last 6 period is 100,12,80,90,110and 70 respectively. the forecast for 7th period on the basis of 5 period moving average will be
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Answer:
Forecasting examples
Forecasting example 1996 UG exam
The demand for a product in each of the last five months is shown below.
Month 1 2 3 4 5
Demand ('00s) 13 17 19 23 24
Use a two month moving average to generate a forecast for demand in month 6.
Apply exponential smoothing with a smoothing constant of 0.9 to generate a forecast for demand for demand in month 6.
Which of these two forecasts do you prefer and why?
Solution
The two month moving average for months two to five is given by:
m2 = (13 + 17)/2 = 15.0
m3 = (17 + 19)/2 = 18.0
m4 = (19 + 23)/2 = 21.0
m5 = (23 + 24)/2 = 23.5
The forecast for month six is just the moving average for the month before that i.e. the moving average for month 5= m5 = 2350.
Applying exponential smoothing with a smoothing constant of 0.9 we get:
M1 = Y1 = 13
M2 = 0.9Y2 + 0.1M1 = 0.9(17) + 0.1(13) = 16.60
M3 = 0.9Y3 + 0.1M2 = 0.9(19) + 0.1(16.60) = 18.76
M4 = 0.9Y4 + 0.1M3 = 0.9(23) + 0.1(18.76) = 22.58
M5 = 0.9Y5 + 0.1M4 = 0.9(24) + 0.1(22.58) = 23.86
As before the forecast for month six is just the average for month 5= M5 = 2386
To compare the two forecasts we calculate the mean squared deviation (MSD). If we do this we find that for the moving average
MSD = [(15 - 19)² + (18 - 23)²+ (21 - 24)²]/3 = 16.67
and for the exponentially smoothed average with a smoothing constant of 0.9
MSD = [(13 - 17)² + (16.60 - 19)² +(18.76 - 23)²+ (22.58 - 24)²]/4 = 10.44
Overall then we see that exponential smoothing appears to give the best one month ahead forecasts as it has a lower MSD. Hence we prefer the forecast of 2386 that has been produced by exponential smoothing.