Question

Use the following time-series data to answer the given questions. Time Period Value 1 25 2 31 3 58 4 62 5 59 6 66 7 72 8 86 9 101 10 97 a. Develop forecasts for periods 5 through 10 using 4-month moving averages. b. Develop forecasts for periods 5 through 10 using 4-month weighted moving averages. Weight the most recent month by a factor of 4, the previous month by 2, and the other months by 1. c. Compute the errors of the forecasts in parts (a) and (b) and observe the differences in the errors forecast by the two different techniques. (Round your answers to 3 decimal places.)

Answer 1

a)4-month moving averages forecast:

period	value(A)	Forecast(F)	|A-F|	(A-F)^2
1	25
2	31
3	58
4	62
5	59	44	15	225
6	66	52.5	13.5	182.25
7	72	61.25	10.75	115.5625
8	86	64.75	21.25	451.5625
9	101	70.75	30.25	915.0625
10	97.00	81.25	15.75	248.0625
		total	106.5	2137.5
		average	17.750	356.250

from above Mean absolute deviation (MAD)=17.750

and mean square error MSE=356.250

b)

fr 4-month weighted moving averages=(4*recent month value+2*previous month value+other months value)/(4+2+1+1)=(4*recent month value+2*previous month value+other months value)/8

from above 4-month weighted moving averages forecast

period	value(A)	Forecast(F)	|A-F|	(A-F)^2
1	25
2	31
3	58
4	62
5	59	52.5	6.50	42.25
6	66	56.125	9.88	97.52
7	72	62.75	9.25	85.56
8	86	67.625	18.38	337.64
9	101	76.625	24.38	594.14
10	97.00	89.25	7.75	60.06
		total	76.13	1217.17
		average	12.688	202.862

from above Mean absolute deviation (MAD)=12.688

and mean square error MSE=202.862

c)

as MAD and MSE values are less for part b) therefore 4-month weighted moving forecast is better