CIMA BA1: BA1 Fundamentals of Business Economics

Module: 19

Moving Averages

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1. Introduction

We have looked at a few methods for coping with variations, but so far these

have assumed a linear trend (straight line). Of course, real life is very rarely

like this. Sometimes graphs look like this:

So, we need something that can cope with wiggles. We have also focussed

a lot on seasonal trends despite recognising that cyclical and random

reasons also occur. Time to put that right!

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2. Moving averages

The moving average is a technique to reduce irregularities and smooth

out the dispersion caused by variations. These components are difficult to

identify, and the moving average technique makes the long-term trend

stand out clearly.

Gavin has been asked by his manager to forecast the results for 20X4. Here

are his results:

Time £m

20X0 Q1 24.6

20X0 Q2 38.4

20X0 Q3 36.9

20X0 Q4 48.0

20X1 Q1 32.3

20X1 Q2 44.8

20X1 Q3 42.0

20X1 Q4 60.3

20X2 Q1 39.8

20X2 Q3 54.9

20X2 Q4 72.8

20X3 Q1 56.9

20X3 Q2 59.1

20X3 Q3 59.9

20X3 Q4 72.0

Three point moving average

Let's get straight into the calculation to demonstrate how moving averages

work - they're much easier to demonstrate than explain!

Let's start by taking the first 3 quarters of figures (those from 20X0) and calculate

an average:

24.6 + 38.4 + 36.9 =33.3

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Next, we move everything on one period, so now we take the last 3 quarters

of 20X0:

38.4 + 36.9 + 48.0 =41.1

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And so, on until we get the 3 point moving averages as follows:

Time £m Moving Av.

20X0 Q1 24.6

20X0 Q2 38.4 33.3

20X0 Q3 36.9 41.1

20X0 Q4 48.0 39.1

20X1 Q1 32.3 41.7

20X1 Q2 44.8 39.7

20X1 Q3 42.0 49.0

20X1 Q4 60.3 47.4

20X2 Q1 39.8 49.2

20X2 Q2 47.6 47.4

20X2 Q3 54.9 58.4

20X2 Q4 72.8 61.5

20X3 Q1 56.9 62.9

20X3 Q2 59.1 58.6

20X3 Q3 59.9 63.7

20X3 Q4 72.0

Notice how we associate our first moving average with 20X0 Q2 (shown in

bold), and the second with 20X0 Q3, those just being the midpoints of the

three items we based our calculation on.

Let's look at this data on a graph. The full line is the original data and the

dotted line the moving average:

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As you can see the moving average smooths out the distortions somewhat

giving a straighter line, although it's far from perfect!

One reason it is still really rather wiggly is because we took an average of 3

quarters, and sales in a business are more likely to vary every year, or 4

quarters. We'd hope that if we used a four-period average we would get a

much smoother line. Let's see.

Four point moving average

Doing the calculation for 4 quarters is a little more complicated.

Let's do our first 4 point moving average from the first 4 quarters (sometimes referred to as the four-quarterly total).

24.6 + 38.4 + 36.9 + 48.0 =37.0

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Next move everything on one period, so now we take the last 3 quarters of

20X0 and the first quarter of 20X1:

38.4 + 36.9 + 48.0 + 32.3 =38.9

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Then we'll add these to our table as follows:

Time

20X0 Q1

£m

24.6

Calculation

20X0 Q2

20X0 Q3

38.4

36.9

37.0

20X0 Q4 48.0 38.9 20X1 Q1 32.3

Notice though that our calculations are not aligned to a particular quarter

this time (unlike the 3 point average). That's a pain as when we do

calculations later we do need them to be aligned.

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The problem is easily solved. If we take the average of 37.0 and 38.9,

we'll get a figure we can associate with 20X0 Q3 (which is midway

between the two and sometimes referred to as the centred eight quarterly

total).

Doing this for all our data we get the following result:

Time

£m

Calculation

Moving Av.

(Trend)

20X0 Q1 24.6

20X0 Q2

20X0 Q3

38.4

36.9

37.0

37.9

20X0 Q4

48.0

38.9 39.7

20X1 Q1

32.3

40.5 41.1

20X1 Q2

44.8

41.8 43.3

20X1 Q3

42.0

44.9 45.8

20X1 Q4

60.3

46.7 47.1

20X2 Q1

39.8

47.4 49.0

20X2 Q2

47.6

50.7 52.2

20X2 Q3

54.9

53.8 55.9

20X2 Q4

72.8

58.1 59.5

20X3 Q1

56.9

60.9 61.6

20X3 Q2

59.1

62.2 62.1

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Time £m Calculation Moving Av. (Trend) 62.0

20X3 Q3 59.9 20X3 Q4 72.0

Let's look at the graph of this:

The moving average (the dotted line) over 4 periods is much smoother

than that for 3, and that's logical as sales are more likely to vary over the

period of a year than over 3 quarters.

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Seasonal variations

We can also calculate seasonal variations using the same method.

Let's say we were using an additive model - the seasonal variation is the

difference between the moving average and the actual figure.

Time

£m

Calculation

Moving

Average

(Trend)

Seasonal

Variation

20X0 Q1 24.6

20X0 Q2 38.4

37.0

20X0 Q3 36.9 37.9 -1.0 38.9

20X0 Q4 48.0 39.7 8.3 40.5

20X1 Q1 32.3 41.1 -8.8 41.8

20X1 Q2 44.8 43.3 1.5 44.9

20X1 Q3 42.0 45.8 -3.8 46.7

20X1 Q4 60.3 47.1 13.2 47.4

20X2 Q1 39.8 49.0 -9.2 50.7

20X2 Q2 47.6 52.2 -4.6 53.8

20X2 Q3 54.9 55.9 -1.0 58.1

20X2 Q4 72.8 59.5 13.3 60.9

20X3 Q1 56.9 61.6 -4.7 62.2

20X3 Q2 59.1 62.1

62.0

20X3 Q3 59.9

20X3 Q4 72.0

As we did in the previous section we can work out an average seasonal

variation.

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As an example, in Quarter 3, we have the seasonal variations of -1.0, -3.8,

and -1.0, giving an average of -1.9.

Doing a similar calculation, we get seasonal variations of:

Quarter 1: (7.6)

Quarter 2: (1.0)

Quarter 3: (1.9)

Quarter 4: 11.6