#### Time series analysis: please note that this lecture relates to Chapter 12 of the Course Notes (and not Chapter 11 as stated in the lecture)

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hlony says

Please make me understand the logic here when calculating seasonal variation,are subtracting actual from the trend or the trend from the actual?

Thanks in advance

johnmoffat says

It is actual minus trend.

However, as it states clearly in the notes, you will not be asked arithmetic on time series analysis.

Chris says

Hi John,

I hope you are well… It’s been a long time since studying this sort of material at school. I just wanted you to clarify if you may for me please.

You said partway through the lecture that you would need to calculate the moving average and then the centered average/trend if its a 4 quarter period. However, if it was a three part period, the trend would already be calculated.

I am somewhat confused. No doubt it is very basic but your help would be much appreciated.

I am now going back to look at F2 – Regression Analysis but as mentioned, your help would be great.

Thank you.

Chris.

johnmoffat says

The reason is the the middle of 1, 2, 3, 4 is in between 2 and 4. However the middle of 1, 2, 3 is 3.

I am happy to explain more, but I do not want to waste your time. As it says in the Course Notes, in Paper F5 you cannot be expected to do calculations. All that is expected is that you are aware of the idea (and even asking that is not very likely in Paper F5).

fabiangrey says

What do you mean by:

“Forecast the Trend, Adjust by reevant average seasonal variation”?

johnmoffat says

The trend is the basic pattern (without the seasonal variation).

You can forecast this, but the actual forecast will be higher or lower than the trend because of the seasonal variation.

So you are being asked to forecast the trend, and then to adjust it (higher or lower) to account for the seasonal variation.

printhan says

proportional (multiplicative) model still in the syllabus??

johnmoffat says

Yes – it is assumed knowledge from Paper F5.

BUT read what it says in the Course Notes – you will not be asked calculations. You are only expected to understand the principles.

Killqa says

Thanks for the lecture but I still have some doubts on the theory behind it. I get the calculation part but at the end where you mentioned that adding the average of the season variation equals zero, what does that means? Very confused about the theory aspect. It would be great if you could explained the link between moving average, centered average and how the average seasonal variation correlate, thanks!

johnmoffat says

Before I answer, do realise that (as it says in the Course Notes) that you will not be asked for detailed calculations on time series in F5. You are only expected to be aware of the idea, because it is all revision from Paper F2 (where it was examined in detail). Also, there is no theory involved. You might be asked as a small part of a question to discuss, but there is no theory – discussion is not theory.

All we are trying to do is estimate what the sales per quarter would have been if there was no seasonality.

You say that you are happy with the arithmetic, and so you will understand that the moving average is simply calculating the average sales per quarter for each successive 12 months. Because of the seasonality, some quarters are higher and some lower, but by calculating the average we are ‘cancelling’ or removing the seasonality.

The problem is, that we want to know what the sales per quarter would have been without the seasonality.

Just suppose there was no seasonality and that they have been increasing steadily each quarter.

Suppose that (quarter by quarter) they were 10, 20, 30 and 40 for each of the first four quarters. We could work out the average per quarter by adding and dividing by 4 and we would get 25. However, this would not correspond with any one quarter – it would be sort of in the very middle of the year.

The same is happening with the moving averages – each average does not correspond to any one quarter.

To make it correspond, we the took the averages of the averages – the centred average – and now the averages do correspond to each quarter. So what we have is an estimate of what the sales per quarter would have been if there was not seasonality – and as we would expect, the pattern (the trend) is a lot smoother and easier to forecast into the future.

The actual sales per quarter are different from the trend – some quarters are higher and some are lower. The differences are due to the seasonality and we call the differences the seasonal variations. Things are not perfect and so some quarterly variations are bigger than others – that is why we calculate the average seasonal variation.

As so why they should add up to zero. Think about this – if you take the average of 10 and 20 you get 15. 10 is 5 below the average and 20 is 5 above the average. The average of those differences ((+5 + -5) / 2) is zero. The same thing is happening with the seasonal variations – because they are differences from an average (some higher and some lower) the averages of these differences should be zero.

Joel Changa says

@johnmoffat thank you Sir for the lectures, they were Great……….i highly appreciate the ares you guys outline (Regression Analysis ; Time Series) that wouldn’t be examinable, as with this this time spent for learning these areas could be spent else-where…….i also acknowledge the fact that i need to have an idea of these aspects.

Thanks John.

faith5 says

Since this time series analysis is not in the syllabus, should I forget about? I don’t really like what happened in the last December questions on the areas of concentration and the rest given.

Thank you

johnmoffat says

Time series is still examinable because it is assumed knowledge from Paper F2.

However the examiner will not ask for any calculations. It is unlikely that anything will be asked, but you are expected to know the idea.

bondservant says

Please be aware that Time Series is no longer in the syllabus

abodinho says

It has been removed from the syllabus as it will be assumed knowledge from F2 syllabus, so it is still examinable.