Question

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

Time Period Value

1 26 2 30 3 57 4 62 5 58 6 65 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

1.) Please find the forecasts below:

Time Period	Value	4-months Moving Average
1	26
2	30
3	57
4	62
5	58	43.75
6	65	51.75
7	70	60.5
8	86	63.75
9	101	69.75
10	97	80.5

2.)

Time Period	Value	4-months Weighted Moving Average
1	26
2	30
3	57
4	62
5	58	59.7
6	65	63.3
7	70	70.7
8	86	75.7
9	101	86.7
10	97	101.6

Given weights as 4,2,1,1

Sum of weights = 7

So, for time period 5 is calulated as:

[(4 * time period 4 value) + (2 * time period 3 value) + ( 1 * time period 2 value) + ( 1 * time period 1 value)] / sum of weights

Similarly, time period 6 is calculated as:

[(4 * time period 5 value) + (2 * time period 4 value) + ( 1 * time period 3 value) + ( 1 * time period 2 value)] / sum of weights

3.) It is clearly visible that there is less deviation in case of weighted moving average than Simple moving average.

To confirm that, We will be comparing Root Mean Square Error(RMSE) for both cases

So, RMSE(simple-moving average)

Time Period	Value	4-months Moving Average	ERROR ^2
1	26
2	30
3	57
4	62
5	58	43.75	203.0625
6	65	51.75	175.5625
7	70	60.5	90.25
8	86	63.75	495.0625
9	101	69.75	976.5625
10	97	80.5	272.25
		Mean Square Error	368.791667
		Root Mean Square Error	19.2039492

So, RMSE(Weighted moving average)

Time Period	Value	4-months Weighted Moving Average	Error ^ 2
1	26
2	30
3	57
4	62
5	58	59.7	2.938776
6	65	63.3	2.938776
7	70	70.7	0.510204
8	86	75.7	105.7959
9	101	86.7	204.0816
10	97	101.6	20.89796
		Mean Square Error	337.1633
		Root Mean Square Error	18.36201

So, for Weighted moving average RMSE is less than Simple moving Average