Question

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?

Answer 1

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

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(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