Using the 911 call data in Problem, forecast calls for weeks 2 through 25 with a trend-adjusted exponential smoothing model. Assume an initial forecast for 50 calls for week 1 and an initial trend of zero. Use smoothing constants of a = .3 and b = .2. Is this model better than that of Problem? What adjustment might be useful for further improvement? (Again, assume that actual calls in week 25 were 85.)
Problem - Emergency calls to the 911 system of Durham, North Carolina, for the past 24 weeks are shown in the following table:
|
Week
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
|
Calls
|
50
|
35
|
25
|
40
|
45
|
35
|
20
|
30
|
35
|
20
|
15
|
40
|
|
Week
|
13
|
14
|
15
|
16
|
17
|
18
|
19
|
20
|
21
|
22
|
23
|
24
|
|
Calls
|
55
|
35
|
25
|
55
|
55
|
40
|
35
|
60
|
75
|
50
|
40
|
65
|
a) Compute the exponentially smoothed forecast of calls for each week. Assume an initial forecast of 50 calls in the first week, and use a = .2. What is the forecast for week 25?
b) Reforecast each period using a = .6.
c) Actual calls during week 25 were 85. Which smoothing constant provides a superior forecast? Explain and justify the measure of error you used.