Question

Consider the following time series data. Week 1 2 3 4 5 6 Value 18 13 17 11 17 15 Calculate the measures of forecast error using the naive (most recent value) method and the average of historical data (to 2 decimals). Naive method Historical data Mean absolute error Mean squared error Mean absolute percentage error

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Consider the following time series data.

Month	1	2	3	4	5	6	7
Value	23	14	19	10	18	23	26

Round your answers to two decimal places.

a. Compute MSE using the most recent value as the forecast for the next period.

Mean squared error is ?

What is the forecast for month 8 ?

b. Compute MSE using the average of all data available as the forecast for the next period.

Mean squared error is ?

What is the forecast for month 8 ?

Answer 1

1)

Naïve method:

Time period	Actual Value(A)	Moving avg. Forecast(F)	Forecast error E=|A-F|	Squared Forecast Error	|A-F|A
1	18
2	13	18	5	25	0.3846
3	17	13	4	16	0.2353
4	11	17	6	36	0.5455
5	17	11	6	36	0.3529
6	15	17	2	4	0.1333
7		15
		Total	23	117	1.65
		Average	4.60	23.40	33.03%
			MAD	MSE	MAPE

Historical data method:

Time period	Actual Value(A)	historical Data Forecast(F)	Forecast error E=|A-F|	Squared Forecast Error	|A-F|A
1	18
2	13	18.00	5.00	25.00	0.38
3	17	15.50	1.50	2.25	0.09
4	11	16.00	5.00	25.00	0.45
5	17	14.75	2.25	5.06	0.13
6	15	15.20	0.20	0.04	0.01
7		15.17
		Total	13.95	57.3525	1.07
		Average	2.79	11.47	21.46%
			MAD	MSE	MAPE

from above:

	naïve	Historical data
MAE	4.60	2.79
MSE	23.40	11.47
MAPE	33.03	21.46

2)

a)

MSE=			55.83
Forecast=			22.33

b)

MSE =			43.96
forecast =			19.00