Please note the data for a Burrito shop which is counting the
number of customers daily.
Brad's Burritos
Period t 1 2 3 4 5 6 7 8 9 10
Observed 108 130 96 144 136 113 120 119 120 106
a. Compute a forecast for the next day by using a 3-day moving
average. What is the
forecast? What is the MAD for the last five observations?
b. Compute a forecast for the number of customers for the next
day using
exponential smoothing with α = 0.3. What is the forecast? What is
the MAD for the last five observations?
The Solution:
(a)
Calculate the forecast using 3-month moving average.
Period |
Data |
Moving average |
1 |
108 |
- |
2 |
130 |
- |
3 |
96 |
- |
4 |
144 |
(108 + 130 + 96)/3 = 111.3333 |
5 |
136 |
(130 + 96 + 144)/3 = 123.3333 |
6 |
113 |
(96 + 144 + 136)/3 = 125.3333 |
7 |
120 |
(144 + 136 + 113)/3 = 131 |
8 |
119 |
(136 + 113 + 120)/3 = 123 |
9 |
120 |
(113 + 120 + 119)/3 = 117.3333 |
10 |
106 |
(120 + 119 + 120)/3 = 119.6667 |
11 |
- |
(119 + 120 + 106)/3 = 115 |
Now Find Absolute Error for each forecast:
Period |
Data |
Forecast |
Absolute Error |
1 |
108 |
||
2 |
130 |
||
3 |
96 |
||
4 |
144 |
111.3333 |
|144- 111.333| = 32.6667 |
5 |
136 |
123.3333 |
12.6667 |
6 |
113 |
125.3333 |
12.3333 |
7 |
120 |
131 |
11 |
8 |
119 |
123 |
4 |
9 |
120 |
117.3333 |
2.6667 |
10 |
106 |
119.6667 |
13.6667 |
11 |
- |
115 |
Forecast = 115.00
MAD for last five observations = (12.3333 + 11 + 4 + 2.6667 + 13.6667) / 5 = 43.6667/5 = 8.73334
===============================================================
(b)
Forecast using smoothening constant 0.3
Period |
Data |
Forecasts |
1 |
108 |
108 |
2 |
130 |
108+0.3⋅ (108−108) =108 |
3 |
96 |
108+0.3⋅ (130−108) =114.6 |
4 |
144 |
114.6+0.3⋅ (96−114.6) =109.02 |
5 |
136 |
109.02+0.3⋅ (144−109.02) =119.514 |
6 |
113 |
119.514+0.3⋅ (136−119.514) =124.4598 |
7 |
120 |
124.4598+0.3⋅ (113−124.4598) =121.0219 |
8 |
119 |
121.02186+0.3⋅ (120−121.02186) =120.7153 |
9 |
120 |
120.715302+0.3⋅ (119−120.715302) =120.2007 |
10 |
106 |
114+0.3⋅ (120−120.2007114) =120.1405 |
11 |
- |
120.14049798+0.3⋅ (106−120.14049798) =115.8983 |
Calculate Absolute Error:
Period |
Data |
Forecast |
Absolute Error |
1 |
108 |
108 |
|108-108| = 0 |
2 |
130 |
108 |
|130 – 108| = 22 |
3 |
96 |
114.6 |
18.6 |
4 |
144 |
109.02 |
34.98 |
5 |
136 |
119.514 |
16.486 |
6 |
113 |
124.4598 |
11.4598 |
7 |
120 |
121.0219 |
1.0219 |
8 |
119 |
120.7153 |
1.7153 |
9 |
120 |
120.2007 |
0.2007 |
10 |
106 |
120.1405 |
14.1405 |
11 |
- |
115.8983 |
Forecast: 115.8983
MAD for the last five observations = (11.4598 + 1.0219 + 1.7153 + 0.2007 + 14.1405) / 5 = (28.5382)/ 5 = 5.70764
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