Question

Use the following time-series data to answer the given questions.

Time Period Value

1 27 2 30 3 58 4 63 5 59 6 67 7 70 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.

Answer 1

Soln,

a) Forcasting for periog 5 through 10 using 4 month moving average

This can be done by formulae,

F₅(5 th time period forcasting data )= (Data1+data2+data 3+ data4)/4

simillarly for rest of the dta till 10th time period.

Time period	Value	4 Month Moving average	Error	Absolute Error
1	27
2	30
3	58
4	63
5	59	44.5	14.5	14.5
6	67	52.5	14.5	14.5
7	70	61.75	8.25	8.25
8	86	64.75	21.25	21.25
9	101	70.5	30.5	30.5
10	97	81	16	16
			MAD=	17.5

MAD= Mean absolute deviation= Mean of Absolute Errors.

b)The Forcasting by 4- Month Weighted moving average can br done by formulae , lets say for 5 th time period.

Ad according to question weight as 4,2,1,1

Similarly each time period forcasting data is calculated.

Time period	Value	4 Month Weighted Moving average	Error	Absolute Error
1	27
2	30
3	58
4	63
5	59	53.125	5.875	5.875
6	67	56.25	10.75	10.75
7	70	63.375	6.625	6.625
8	86	67	19	19
9	101	76.25	24.75	24.75
10	97	89.125	7.875	7.875
			MAD=	12.48

c) The Error calculated in part a and part b is tabulated above.

Here we can see that by Forcasting through 4 Month moving average the mean error calculated was 17.5, and MAD or mean error calculated if forcasting done by 4 month weighted moving average the error of 12.48 was calculated.

If we compare both the errors we can find that 4 Month weighted moving average forcasting method is more accurate than 4 Month moving average forcasting method.