Question

Consider the following time series data.

Week	1	2	3	4	5	6
Value	19	12	15	11	17	15

Using the naïve method (most recent value) as the forecast for the next week, compute the following measures of forecast accuracy:

Mean absolute error (MAE)

Mean squared error (MSE)

Mean absolute percentage error (MAPE)

Round your answers to two decimal places.

MAE =

MSE =

MAPE =

Using the average of all the historical data as a forecast for the next period, compute the same three values. Round your answers to two decimal places.

MAE =

MSE =

MAPE =

Answer 1

using naive method

MAE =sum(|y-y^|)/n=22/5=4.4

MSE =sum(|y-y^|)²/n=114/5=22.8

MAPE =(100*|y-y^|/y)n=163.32/5=32.66

week	value (y)	naïve (y^)	E=y-y^	|E|	E2	100*|E|/y
1	19
2	12	19	-7	7	49	58.33333
3	15	12	3	3	9	20
4	11	15	-4	4	16	36.36364
5	17	11	6	6	36	35.29412
6	15	17	-2	2	4	13.33333
MEAN=	14.83	14.80	-0.80	4.40	22.80	32.66

(second part) using average method

MAE =1.83

MSE =5.49

MAPE =14.69

week	value (y)	average(y^)	E=y-y^	|E|	E2	100*|E|/y
1	19
2	12	14.83	-2.83	2.83	8.0089	23.58333
3	15	14.83	0.17	0.17	0.0289	1.133333
4	11	14.83	-3.83	3.83	14.6689	34.81818
5	17	14.83	2.17	2.17	4.7089	12.76471
6	15	14.83	0.17	0.17	0.0289	1.133333
MEAN=	14.83	14.83	-0.83	1.83	5.49	14.69
sum=	70	74.15	-4.15	9.17	27.4445	73.43289