CIMA BA1 Syllabus C. Informational Context Of Business - Additive And Multiplicative Models - Notes ^{6 / 10}

Seasonal variations arise in the short-term

It is very important to distinguish between trend and seasonal variation. 

Seasonal variations must be taken out, to leave a figure which is indicating the Trend.

Methods of calculating Seasonal variation:

1. Additive model

2. Proportional (multiplicative) model

Additive model

This is based upon the idea that each actual result is made up of two influences.

Time series = Trend (T) + Seasonal Variation (SV)

Additive model - Steps

1. Step 1

   Identify the trend

   using Centred moving averages

2. Step 2

   Deduct the Trend from the time series data to obtain the Seasonal variation

   the logic here is that if Time series = Trend + Seasonal variation then re-arranging this gives:

   Seasonal variation = Time series (Y) - Trend (T)

Illustration

Calculate the average seasonal variations from the following data.

The multiplicative model

The additive model assumes that seasonal variation does not increase over time.

This is unlikely — for example, companies that are growing rapidly will have increasing sales figures and therefore higher seasonal variations too.

This drawback of the additive model is picked up by the Multiplicative model.

The multiplicative model is generally considered to be better as it assumes forecast seasonal components are a constant proportion of sales.

Time series = Trend x Seasonal Variation (SV)

Multiplicative model - Steps

1. Step 1

   Identify the trend

   using centred moving averages

2. Step 2
    
   Divide the time series by the trend data to obtain the seasonal variation

   the logic here is that if time series = trend x seasonal variation then re-arranging this gives:

   Seasonal variation = Time series (Y)  / Trend (T)

Illustration - Multiplicative model

Illustration - Additive model

The trend for train passengers at Paddington station is given by the relationship:

y = 5.2 + 0.24x

y = number of passengers per annum

x = time period (2011 = 1)

What is the trend in 2019?

• Solution
  If x = time period (2011 = 1), then 2019 will be 9.

  y = 5.2 + 0.24 x 9 = 7.36

Illustration - Multiplicative model

A company uses a multiplicative time series model.

Trend = 500 + 30T

T1 = First quarter of 2010. 

Average seasonal variation:

1st Q = -20
2nd Q = +7
3rd Q = +16
4th Q = -1

What is the sales forecast of the 3rd Q of 2012?

Solution

If T1 = First quarter of 2010, then 3rd Quarter of 2012 will be 11.

T = (500 + (30 x 11)) x 116% = 963