1. Time Series Analysis Predicting future sales from past numbers

2. What is it? This is not as difficult as it first appears so do not panic! It is used to forecast future sales from past data. If we have a sales pattern that has grown like this one...

3. Sales Time

4. Then we can predict the future Sales Time N.B. May not always happen!

5. But what if it looked like this? Sales Time

6. This is where time series analysis comes in. It ‘irons out’ the peaks and troughs in data to give a roughly smooth line which you can then extend into the future N.B. The further into the future you go the less reliable the extrapolation becomes.

7. How does it do this? It does this by taking an average of figures over a time period, for example an average of the 4 quarters in a year. Then the first time period is dropped off the average and the next one is added.

8. For example Mon Tues WedFirst number Tues Wed ThursSecond number Wed Thurs FriThird number Thurs Fri SatFourth number And so on…. It is called a moving average.

9. MonthActual sales 4 quarter moving average Jan10 Feb11 Mar13 April7 May12 10+11+13+7 4 =10.25 For example…. It is important that the answer is between feb and March and not with either one. This is called Centering

10. Then… MonthActual sales 4 quarter moving average Jan10 Feb11 Mar13 April7 May12 11+13+7+12 4 =10.75 10.25

11. And then… MonthActual sales4 quarter moving average Feb11 Mar13 April7 May12 June13 13+7+12+13 4 =11.25 10.25 10.75

12. Until… MonthActual sales4 quarter moving average Jan10 Feb11 Mar13 April7 May12 June13 July16 Aug6 Sept13 Oct15 Nov16 Dec9 10.25 10.75 11.25 12 11.75 12 12.5 12

13. You can see it leads to a flatter line

14. If it is still not flat enough… Then you can take an average of the moving average (usually only 2 each time) This also centres the data for you automatically. (So it falls exactly on a month and not between two)

15. Like so… MonthActual sales4 quarter moving average 8 quarter moving ave Jan10 Feb11 Mar1310.5 April711 May1211.625 June1311.825 July1611.825 Aug612.5 Sept1312.5 Oct1512.25 Nov16 Dec9 10.25 10.75 11.25 12 11.75 12 12.5 12

16. We can now look into the future ?

17. How accurate? How often did the actual sales coincide with the trend? Why should this start to happen in the future?

18. Variation Calculate the difference between the moving ave figures and the actual numbers. Positive and negatives are important. This is why we centred the data!

19. MonthActual sales 4 quarter moving average 8 quarter moving ave Variation Jan10 Feb11 Mar13-2.5 April7-4 May120.375 June131.125 July164.125 Aug6-6.5 Sept130.5 Oct152.75 Nov16 Dec9 10.25 10.75 11.25 12 11.75 12 12.5 1210.511 11.625 11.825 11.825 12.5 12.5 12.25

20. Therefore… -2.5-4+0.375+1.125+4.125-6.5+0.5+2.758=-0.515 Therefore, on average the actual line is 0.515 below the trend line. So we should allow for this in our extrapolation

21. Variation Then find the average variation, and just add (or subtract) it to the extrapolated prediction. This will on average cover the variations between the trend and the actual numbers.

22. We can do better however. Seasonal Variations

23. Seasonal what? Many firms have busy and quiet times For example….

24. We can take account of this If sales in January are always low then we can make our predictions more accurate by taking this into account. Instead of working out the variance for all time periods we could look at the variance for Januarys, then Februarys, then all Marches and so on.

25. How? In the same way. Find the average variation for the time you are interested in and then add it to (or take it away from) your prediction.

26. Beware Past performance does not mean it will carry on for ever The further into the future you go the less reliable it becomes.