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