b. Calculate the exponential smoothing with trend forecast for these data using
ID: 388337 • Letter: B
Question
b. Calculate the exponential smoothing with trend forecast for these data using an of 0.30, a of 0.30, an initial trend forecast (TI) of 1.00, and an initial exponentially smoothed forecast (F1) of 33. (Round your intermediate calculations and answers to 2 decimal places.) Month FIT 4 59 10 c-1. Calculate the mean absolute deviation (MAD) for the last nine months of forecasts. (Round your intermediate calculations and answers to 2 decimal places.) MAD Single exponential smoothing forecast Exponential smoothing with trend forecastExplanation / Answer
b. Exponential Smoothing with trend forecast:
= 0.30
= 0.30
T1 (initial trend forecast) = 1.00
F1 (initial exponentially smoothed forecast) = 33
Demand for last 10 months:
Month
Actual Demand
1
34
2
37
3
34
4
35
5
38
6
36
7
39
8
39
9
41
10
41
Exponential smoothing with trend forecast is the sum of exponential smoothing of forecast and exponential smoothing of trend.
FIT1= F1 + T1 = 33 + 1 = 34
Smooth Forecast of period is taken by multiplying factor to error in previous forecast ( actual - exponentially smoothened forecast of previous period) and adding to the previous exponentially smoothened forecast with trend
Ft+1 = FITt + * (At - FITt)
Similarly for trend, the forecast value is derived by multiplying factor to difference between present and previous forecast with trend) and adding the last trend value.
Tt+1 = Tt+ * (Ft+1- FITt)
Use this formula for all the periods to forecast data
2) Mean Absolute Deviation (MAD) is the sum of all absolute values of all the errors and dividing the error by the total no. of periods as given so as to understand the deviation and the average deviation of the absolute error from the average.
For Single exponential smoothing forecast :
MAD = sum of |A – Ft+1|
No. of periods
Month
Actual Demand
F
Error = A - F
Absolute error
1
34
33.00
1.00
1.00
2
37
34.00
3.00
3.00
3
34
35.60
-1.60
1.60
4
35
35.95
-0.95
0.95
5
38
36.31
1.69
1.69
6
36
37.35
-1.35
1.35
7
39
37.54
1.46
1.46
8
39
38.43
0.57
0.57
9
41
39.10
1.90
1.90
10
41
40.17
0.83
0.83
Total
14.35
Average of Total of absolute error for only 9 periods will give MAD
MAD = sum of |A – Ft+1| = 13.35/9 = 1.48
No. of periods (2 -9)
For exponential smoothing with trend forecast:
Average of Total of absolute error for only 9 periods will give MAD
MAD = sum of |A – Ft+1| = 11.95/9 = 1.33
No. of periods (2 -9)
Month
Actual Demand
1
34
2
37
3
34
4
35
5
38
6
36
7
39
8
39
9
41
10
41
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