Question

Daily high temperatures in St. Louis for the last week were as​ follows:

95​, 92​, 93​, 95​, 95​, 86​, 95 ​(yesterday).​

a) The high temperature for today using a​ 3-day moving average ​=   ? degrees ​(round your response to one decimal​ place).

​b) The high temperature for today using a​ 2-day moving average ​= ? degrees ​(round your response to one decimal​ place).​

c) The mean absolute deviation based on a​ 2-day moving average​ = ? degrees ​(round your response to one decimal​ place).​

d) The mean squared error for the​ 2-day moving average​ = ? degrees squared2 ​(round your response to one decimal​ place).​

e) The mean absolute percent error​ (MAPE) for the​ 2-day moving average​ = ? ​%(round your response to one decimal place​).

Answer 1

Let the daily high temperature be denoted by A and Forecast by F

(a) For 3 day moving average forecast, F_t = (A_t-1 + A_t-2 + A_t-3)/ 3 = (95 + 86 + 95)/3 = 92

(b) For 2 day moving average forecast, F_t = (A_t-1 + A_t-2)/2 = (95 + 86)/2 = 90.50

(c) mean absolute deviation is the average of absolute error in forecast -

Day	Temperature	Forecast	Error	Absolute Error
1	95
2	92
3	93	93.5	-0.5	0.5
4	95	92.5	2.5	2.5
5	95	94	1	1
6	86	95	-9	9
7	95	90.5	4.5	4.5
				3.5
				MAD

Hence, MAD = 3.5

(d) mean squared error is the average of squared error

Day	Temperature	Forecast	Error	Squared error
1	95
2	92
3	93	93.5	-0.5	0.25
4	95	92.5	2.5	6.25
5	95	94	1	1
6	86	95	-9	81
7	95	90.5	4.5	20.25
				21.75
				MSE

Hence, MSE = 21.8

(e) mean absolute percent error is the average of absolute percentage error

Day	Temperature	Forecast	Error	absolute % error
1	95
2	92
3	93	93.5	-0.5	0.54
4	95	92.5	2.5	2.63
5	95	94	1	1.05
6	86	95	-9	10.47
7	95	90.5	4.5	4.74
				3.88
				MAPE

Hence, MAPE = 3.9%