1. avatar says


    Can you kindly show me calculation for Q1 under TEST on pg 107 i agree with what you’ve said on the video that the amount for Q4 should be -7.6 but for exam purpose in case you are not given a question in multiple choice Question format

    • Profile photo of John Moffat says

      Questions on time series will be in multiple choice format!

      The seasonal variations should add up to zero (using the additive model).

      So 5.8 – 8.4 + 10.2 + X = 0, where X is the season 4 variation.

      It is then basic arithmetic to calculate X :-)

  2. avatar says

    Dear Sir,

    Sorry to bother you again.

    The answer to the question from a June 2011 exam paper was 517 units (400+(10*7)*1.1, but the response received calculated to 480 units. Could you please explain how 1.1 was calculated.

  3. avatar says

    Dear Sir,

    Would you please assist me with working out this question:

    A company uses a multiplicative time series to forecast sales. The trend in sales is linear and is described by the following equation

    Trend = 400 + 10 T
    where T = 1 denotes the first quarter of 2010, T = 2 denotes the second quarter of 2010 etc.

    The average seasonal variations are as follows:

    Quarter 1 2 3 4
    % Variation -30 +40 +10 -20

    What is the sales forecast for the third quarter of 2011?

    • Profile photo of John Moffat says

      The last quarter of 2010 is T=4. the first quarter or 2011 is T=5.
      So…the third quarter is T=7

      Put T = 7 in the equation and that will give you the trend.

      Because the variation for quarter 3 is +10, add 10 to the trend and you will have the forecast.

  4. avatar says

    Dear Sir,

    I perfectly understand the calculation of time series and seasonal variations. But can you please explain me how this variation is help full for me. Like if i expecting average sales for next year 250,000 every quarter i might forecast the quarterly sales by the variation. Like Q1 95 % of 250,000 etc….
    Please explain!!!

    • Profile photo of John Moffat says

      It can be useful in budgeting if you are wanting to forecast sales per quarter.

      It is also used by governments etc when looking at such things as number of people unemployed. In the UK, for example, unemployment is always lower in summer because people get temporary work in farms. It is therefore not valid to compare the numbers for spring and summer and say that overall unemployment is falling. So they adjust the figures for seasonal variations and it is then a better comparison.

  5. avatar says

    Hi, in Moving Averages – Example 1. (pg 100).

    I went ahead and try to verify the trend vs actual for 2002 Q3.
    We figured that the average seasonal variation for Q3 is -3.94 and I calculated the average trend increment is 3.04.

    Trend in 2002 Q2 was 107.25, therefore trend in 2002 Q3 should be 107.25 + 3.04 = 110.29.

    Actual in 2002 Q3 should be 110.29 (Trend) + -3.94 (Avg seasonal variation) = 106.35. However, the actual sales that we were given was 103.

    Could you please let me know what is causing the discrepancy? or if I’m doing this incorrectly.

    Thanks a lot.

  6. avatar says

    Great lecture!

    I found it really useful to put the numbers in excel and do the calculations (using =AVERAGE) to show the data graphically. Plot the MAs and CAs on a chart too to graphically show the variances.

    • Profile photo of John Moffat says

      It is because the seasonal variations are all above or below the averages. Some are higher than everage and some are lower that average, and because of the they should add up to zero.

      Does that make sense? :-)

      • Profile photo of Javeria says

        Yes thank you so much…. one little thing we have alot of questions in our revision kit on multiplicative model and i cant find a video explaining that, i just want to know is it important and can we expect a lot of questions based on that in exams …… thanks you =)

      • Profile photo of John Moffat says

        The multiplicative model is covered in this video (after the additive model).
        I would not expect there to be lots of questions on time series, but there are certainly likely to be some questions – one either or both of the two models.

    • Profile photo of Rana Nabeel says

      Slam… These should add up to zero as the trend is between high and low averages, and we have four quarters in a year among them two are higher than average and two are lower than average … so if we see the scenario in an “ideal way” then we come to conclusion that with the value the trend gets higher in “first quarter” it should get lower with same value in the 2nd quarter .. and respectively same in 3rd and 4th quarter so adding up these should result in a perfect zero(Ideal Case)..

      Hope the answer of the question is satisfactory.. :)

  7. avatar says

    Hello John, just for myself to not be confuse is there mistake done in sample 2 calculation multiplicative method? quarter 4: actual / trend should be 98% and in your case its 102% I presume you divide trend/ actual? I am wrong?

    • Profile photo of John Moffat says

      I think you mean slightly different from what you wrote :-)

      What you do to make a forecast is first of all forecast the trend (and this would be the same whether you were using multiplicative or additive), and then you would adjust the trend forecast by the seasonal variation to get the ‘actual’ forecast.

      There are several ways you could forecast the trend, but for exams you would effectively use the high low method. In example 1, the trend values increase from 86.00 to 107.25 (which is an increase of 21.25) over 7 quarters (although their are 8 values, there are 7 increases). So on average it is increasing by 21.25 / 7 = 3.036 per quarter.

      If we want a forecast for qtr 1 of 2003, then this is 3 quarters away from the last trend value we have (quarter 2 of 2002) and so we take 107.25 + (3 x 3.036) = 116.36.
      This is a trend forecast, but we need now to adjust by the seasonal variation.

      Using the additive model, in qtr 1 the actual is on average 0.06 more than the trend, so the forecast would be 116.36 + 0.06 = 116.96

      Using the multiplicative model, qtr 1 is 100% of the trend, and so the forecast would be 100% x 116.36 = 116.36

    • Profile photo of John Moffat says

      Some are higher than average and some are lower than average – however the total difference should be zero.

      Suppose you had two numbers – 70 and 80. The average of the two is 75.

      The difference between the first number and the average is -5
      The difference between the second number and the average is +5

      The total of the differences = -5 +5 = 0

  8. avatar says

    Thanku Open Tuition was breaking my head trying to understand Seasonal Variations,after watching this I understood in 5 mins..U r grt help for people doing self study..Thanku again.

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