### Syllabus B2l)

Use trend and seasonal variation (additive and multiplicative) to make budget forecasts.

### Trend and Seasonal Variations

#### 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 might be taken as indicating the trend (deseasonalised data).

One such method is called moving averages.

A moving average is an average of the results of a fixed number of periods, i.e. the mid-point of that particular period.

Please note that when the number of time periods is an even number, we must calculate a moving average of the moving average.

This is because the average would lie somewhere between two periods.

#### Seasonal Variations

These seasonal variations can be estimated using the additive model or the proportional (multiplicative) model.

#### The additive model

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

Actual = Trend + Seasonal Variation (SV) + Random Variations (R)

The SV will be expressed in absolute terms. Please note that the total of the average SV should add up to zero.

#### Illustration - Additive model

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

y = 5.2+0.24x

y = number of passengers per annum

x = time period (2010 = 1)

What is the trend in 2018?

**Solution**

y = 5.2+0.24(9) = 7.36

#### The multiplicative model

Actual = Trend × SV factor x Random Variations

The SV will be expressed in proportional terms, e.g. if, in one particular period the underlying trend was known to be $10,000 and the SV in this period was given as +12%, then the actual result could be forecast as:

$10,000 × 112/100 = $11,200.

Please note that the total of the average SV should sum to 4.0, 1.0 for each quarter.

#### 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**

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