# Time Series analysis

#### 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)

• 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.

1. 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!

• 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.

2. 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.

3. 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

• 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.

• says

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

4. says

hello i have problem with the question that came in the June 2012 exam. i have problems with this bit
The average seasonal variations can now be calculated to see whether any adjustment to the percentages is required, since
they must be 4•0 in total.
Since the averages total 4•0057, each one needs to be reduced by 0•0016
Q1 Q2 Q3 Q4
2010 0•9080 1•0820
2011 1•1228 0•8989 0•9032 1•0777
2012 1•1256 0•8932
Total 2•2484 1•7921 1•8112 2•1597
––––––– ––––––– ––––––– –––––––
Average 1•1242 0•8960 0•9056 1•0799 4•0057
––––––– ––––––– ––––––– –––––––
Rounded 1•1228 0•8946 0•9042 1•0785 4•0001
The difference of 0•0001 is due to rounding and can be ignored.
The average trend of the centred moving averages is (1,287•5 – 1,068•75)/5 = 43,750 units.
Therefore forecast centred moving average for Q3 in 2012 = 1,287,500 + 43,750 = 1,331,250.
Adjusted for seasonal variation: 1,331,250 x 0•9042 = 1,203,716•25 units.
Forecast centred moving average for Q4 of 2012 = 1,287,500 + (2 x 43,750) = 1,375,000.
Adjusted for seasonal variation = 1,375,000 x 1•0785 = 1,482,937•5 units.
can you help explain it to me please

• says

@chiclarence, I am not sure which bit you are having problems with.

Are you happy with the way that the seasonal variations have been calculated?
In each case it is actual divided by the trend.

Since some variations are more than 1 and some are less than 1, they should add up to 4. They never will because the first two seasons and last two seasons were used in calculating the trend, but could not be used in calculating the seasonal variations.

So, because the total is not 4 then have all be adjusted by one quarter of the difference so that they do add up to 4.

The trend has been forecast assuming it is linear. (The trend is the centred moving average). So because on average it has increased by 43,750 the future forecasts have been made by adding on 43,750 each quarter.

Because those are forecasts of the trend, it is then necessary to adjust by the seasonal variation to arrive at a final forecast. Since on average the seasonal variation for quarter 3 is 0.9056, the actual forecast is 0.9056 of the trend forecast.

Have you watched my lecture on time series?

• says

@johnmoffat, jes John i have watched the video and i am comfortable with the way the average seasonal variations have been calculcated: i know the actual has to be divided by the trend in the multiplicative model but i am not comfortabel with this
Since the averages total 4•0057, each one needs to be reduced by 0•0016
where is the 0.0016 from
secondly i dont understand this bit
Total 2•2484 1•7921 1•8112 2•1597
––––––– ––––––– ––––––– –––––––
Average 1•1242 0•8960 0•9056 1•0799 4•0057
––––––– ––––––– ––––––– –––––––
Rounded 1•1228 0•8946 0•9042 1•0785 4•0001

precise ly i dont understand how the rounded figurs came from:
also theis line
The average trend of the centred moving averages is (1,287•5 – 1,068•75)/5 = 43,750 units.
Therefore forecast centred moving average for Q3 in 2012 = 1,287,500 + 43,750 = 1,331,250.
where is the (1287.5-1.068.75)/5 from and the figure of 1287500 is for which quarter that is being adjusted
cheers

• says

@chiclarence, Since the averages total 0.0057 more than they should do, each of them has been reduced by one quarter of this. (0.0057 /4 = .0014). The 0.0016 is a typing error – if you check you will see that in fact each of them has been reduced by 0.0014.

The first centred moving average (trend) in the question is 1068.75 and the last one is 1287.5. So over 5 quarters it has increased by 1287.5 – 1068.75 = 218.75. Since this os over 5 quarters, the average increase per quarter is 218.75 / 5 = 43.75 (or 43,750).

For forecasting it is assumed therefore that it continues to increase by 43.75 per quarter, as explained in my previous answer.

5. Could you not just work out the moving average over 3 quarters instead of 4 and then it’s already centred albeit with slightly different figures?
It’s still a consistently upward trend although it’s not quite so smooth.

thanks

• says

@andreasmacfarlane, No. The reason is that the seasonality is occurring over a year, and so it is necessary to take the averages over a twelve month period each time.

• @johnmoffat, Thanks John. That makes sense now.

6. says

Hello,
I have a question about example2 of the Course notes(page 61, chapter12). We divide the number of units by 100 just to be easier to make the calculations, but why do we divide the costs by 1000 and not by 100(the answer is on page 118)?
Thanks.

• says

@mdmkd, It does not matter. You do not have to divide the costs and the units by the same number. All that matters is that you divide all the units by the same number; and that you divide all the costs by the same number.

• says

@anatuly007, Consolidations are not in Paper F5
Depending on which accounting paper you are taking, you should look at the F3 pages or the F7 pages.

7. says

Can i ask a question please? why in the multiplicative model of average seasonal variations the figures don’t have a + or – sign in front of them please? for eg in the additive model when we deducted trend from sales, if trend was higher than that had a – sign.

• says

@eley, It is because the multiplicative method is showing the actual as a percent of trend.
If the actual is less than the trend then it will be less than 100% (not negative)
If the actual is more than the trend then it will be more than 100% (not positive),

8. says

I have the same problem locating F2 Regression Analysis ! can anyone help to get the name of the lecture or please post link here??

Thanks.

• says

@mansikhusi, If I am not late to reply for your query ,Regression Analysis Leture is found in ACCA F2 Chapter 17 Semi- Variable Costs(Business Mathematics) .Very interesting lecture by John Moffat.

Best of Luck

• says

@Et, hello! and in which particular lecture of chapter 17 F2? there are 4 videos there.. or is that better to study all 4 lectures?
best wishes for the exam!

• says

@Evgenia, Come on Evgenia …. If I were you I would have given it a glance before I post a query. To my knowledge all 4 are important(really are) as they are also in F5 syllabus.High low,Regression analysis( which is in part C) and Time Series.

I Hope this helps

9. says

I cant locate the F2 Regression Analysis lecture that you recommended, can you advise what the name of this lecture is?

• says

@sheila01, If I am not late to reply for your query ,Regression Analysis Leture is found in ACCA F2 Chapter 17 Semi- Variable Costs(Business Mathematics) .Very interesting lecture by John Moffat.

Best of Luck