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

Question

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

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.

Time Period Value 1 26 2 30 3 57 4 62 5 58 6 65 7 70 8 86 9 101 10 97

Explanation / Answer

1.) Please find the forecasts below:

2.)

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)

So, RMSE(Weighted moving average)

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

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

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