P3: Seasonal Variation

1st u have to calc the trend (general increase/decrease in the time series data, without the seasonal effect). To calc the trend u have to use the 4 quarter moving avg (if there is 4 seasons). Calc moving avg is simply cum avg by constantly adding another period and dropping first period. (i.e avg of periods 1-4, then avg 2-5). This is done to align the avg with one of the periods provided, otherwise it is not really possible). By doing this u will in fact be having an 8 period moving average: 1-4, 2-5, and moving on).

After getting the trend, u have to subtract the trend from the actual data provided for each period except the 1st two periods (bcz no trend will be available for them) to get the actual seasonal variations. Note, however that for each quarter 3, e.g, SV will be different. So u have to avg all the Q3 SVs to get the avg seasonal variation. This will then be slightly adjusted so that when all the avg SVs of all quarters r added, they should equal 0.

Sorry for such messy explanation but it is step by step guide that may help u understand.
But note that you will not need to calc it in exam. just have to analyse the Time series spreadsheet data provided. So a summary of the above may help u explaining the calc if req.

If u have difficulty understanding any part, just state the part and i should clarify it further.

The following illustration will clear all ur doubts:
Actual 8 Q M Avg Variation
Sales (trend)

2001 Q1 120
Q2 110
Q3 115 118 -3
Q4 123 119 4
2002 Q1 125 say121 4
Q2 117 say 123 -6
Q3 119 say 124 -5
Q4 128
2003 Q1
Q2
Q3 say -4
Q4

The seasonal variation will be the average of all q3 variations presented above: -(3+5+4)/3
= -4. However this and all the other quarter variations for the period should net to 0. If this not the case then a small adj is made to make this actually happen:

e.g Q1 Q2 Q3 Q4 Total
SV 3 2 -4 -2 -1
Adj 0.25 0.25 0.25 0.25 1
Adj SV 3.25 2.25 -3.75 -1.75 0

Hence the SV for Q3 is -3.75 (not -4 as before). This -4 I may be wrongly called avg SV when I should have called it Variation simply (so sorry for the confusion).

The final part is to calc the residual which is simply:

for 2002 Q3 : actual sales (119) – trend (124) – SV (-3) = -2
This implies that the actual sales fig for 2002 Q3 is in fact the trend +/- SV +/- Res.
checking: (124 -3 -2) = 119.

Hope this is helpful and clears any remaining doubt u may have.
N.b: this is very technical stuff to explain in writing. U just have to understand the mechanics behind the calc and will rather have to analyse it exam (calc not needed).

If still something is not clear, feel free to make me know i shall be happy to help u, not only in TS analysis but any topic in P3.