BUSINESS ADMINISTRATION AND MANAGEMENT STUDIES: PRACTICAL APPROACH TO MOVING AVERAGE IN MANAGERIAL ECONOMICS

# Consider the following data for sales of product ‘X’ for the period September 2012 to August 2015 (given as quarter 12)

Quarter	1	2	3	4	5	6	7	8	9	10	11	12
Sales (‘000 units )	20	22	23	24	18	23	19	17	22	23	18	23

Analyze the three quarterly and five quarterly moving average forecast for the 13^th quarter and verify that which forecast is more consistent (or better).

Solution :

In order to solve this problems,

You must first of all know ...........What is moving average ?

Moving average is one of the important analytical tool for forecasting. It is one of the simplest smoothing technique. It is also called ‘Moving Mean’ or ‘Rolling Mean’.

This is used to smoothen short-time fluctuations. It filters random “white noise” from the data.

The forecast values of a time series in a given period (may be given in month, quarter or year) = Average value of time series in a number of previous periods.

Here, Smoothing Techniques is one of the forecasting method that helps to forecast the value of time series on the basis of some given past values. It is useful when there is little trend or seasonal variations in the time series but with large random variations. The method is used to cancel the effect due to random variation.

Next thing you must know is ..........What is three- period moving average?

It means, the forecast value of time series of next period that is equal to the average value of time series in the previous three periods.

Similarly, What is five-period moving average?

It means, the forecast value of time series of next period that is equal to average value of time series in the previous five periods.

Note:

The greater the number of periods used in the moving average, the greater is the smoothing effect. Each new observation receives less weight.

Three-quarter and Five-quarter moving average forecast and comparison:

For this, follow the following three simple steps :

Steps :

1. First write the details given in the question in tabular form (i.e. quarter in first column and sales in second and so on as shown below).

- For three-quarter moving average forecast and comparison :

Leave first three column blank.

Add first three period sales data and divide it by three [eg. (20 + 22 + 23 ) / 3 = 21.67 (approx..) ]

Then write the obtained forecasted values of three quarter in corresponding appropriate coloumn ( Three-quarter MA forecast = F ) in fourth quarter. Here, MA means Moving Average.

Continue this process till 12^th quarter.

Similarly, you will obtain the value of 13^th quarter [i.e (23 +18 +23) / 3 = 21.33 ] .

Compute A – F ( i.e Sales (‘000 units ) - Three-quarter MA forecast ).

Compute its square and find the sum of all quarters. Why ? Because the forecast difference or error (A – F ) is squared to penalize larger errors proportionately more than smaller errors.

- For Five-quarter moving average forecast and comparison:

Leave first five column blank.

Add first five period sales data and divide it by five [eg. (20 + 22 + 23 + 24 +25 + 18 ) / 5 = 21.4 (approx..) ].

Then, write the obtained forecasted values of five quarter in corresponding appropriate column ( Five-quarter MA forecast = F ) in sixth quarter. Here, MA means Moving Average.

Continue this process till 12^th quarter.

Similarly, you will obtain the value of 13^th quarter [i.e (17 + 22 +23 +18 + 23) / 5 = 20.6 ] .

Compute A – F ( i.e Sales (‘000 units ) - Five-quarter MA forecast ).

Compute its square and find the sum of all quarters.

2. Compute RMSE (Root- mean-square error (RMSE )

3. Give the decision on the basis of RMSE

Step. 1. Details in Tabular Form :

Quarter	Sales (‘000 units ) = A	Three-quarter MA forecast = F	A – F	( A – F )²	Five-quarter MA forecast	A - F	( A – F )²
1	20	-	-		-
2	22	-	-		-
3	23	-	-		-
4	24	21.67	2.33	5.4289	-
5	18	23	-5	25	-
6	23	21.67	1.33	1.7689	21.4	1.6	2.56
7	19	21.67	-2.67	7.1289	22	-3	9
8	17	20	-3	9	21.4	-4.4	19.36
9	22	19.67	2.33	5.4289	20.2	1.8	3.24
10	23	19.33	3.67	13.4689	19.8	3.2	10.24
11	18	20.67	-2.67	7.1289	20.8	-2.8	7.84
12	23	21	2	4	19.8	3.2	10.24
				∑ (A-F )²= 78.3534			∑ (A-F )²= 62.48
13	-	21.33			20.6

Step. 2 Computation of RMSE :

It helps to find out the weighted average error in the forecast.

For Three-quarter moving average:

that is,

For Five-quarter moving average:

that is,

3. Decision on the basis of RMSE :

Which of these moving average is better ?

For this we have to ,

Compare Root- mean-sqaure error (RMSE ) of each forecast.( i.e Three-quarter moving average with Five-quarter moving average ).

Then, use the moving average that has smallest RMSE.

Here, the RMSE of Three-quarter moving average is less than RMSE of Five-quarter moving average by 0.4 (2.95 < 2.99).

Therefore, the Three-quarter moving average forecast is

Marginally better

More confident

More consistent

- than the Five-quarter moving average forecast.

NOTE :

# The above problem is taken from the question asked in Managerial Economics to their MBS post graduates by Faculty of Management, Tribhuvan University in 2015.

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