1. Analysis of Time Series
For AS90641
Part 3
Reporting
This presentation makes some suggestions for writing up the results in a report format.
September 2005
Created by Polly Stuart

2. Beginnings
You have already done most of the analysis for the retail clothing sales data
Now you need to write the report.
Open a Word document and head it up.
Copy across the spreadsheet that you produced using the previous presentation.
It is desirable to transfer results into a word document to make the report more coherent.
The spreadsheet and graphs produced form the previous presentation are used.

3. Report
The report needs to focus on the validity of the analysis you have done
Every comment you make needs to be justified by referring to your analysis

4. Step 1: Constant dollars
You need to justify why you used constant dollars.
The discussion in the last presentation will help you.
Make sure you relate to the context.
Drawing a graph to compare the original data and constant dollar data may be useful.
Every step needs to be commented on and justified. Students may need to be reminded of why deflation can give more useful results in some cases. There is a link to some other material on indexes on the webpage.

5. Step 2: Discuss each component of the data
Identify the trend in context.
Identify and describe the seasonal pattern.
Describe the pattern of the irregular and identify possible outliers.
See if there are any long term cycles in your data
This combines describing the trend (covered in the first presentation) with examination of the other components. The graphs done previously can be copied across and the features described.
Display your graphs as evidence for your comments.
Be specific, think about the context.

6. Part 3: Forecasting
Justify the model you are using for the forecast by looking at the graphs of each model.
Choose the best and use it to make your forecast.
How good an estimate of the seasonal variation did you have?
Think about how far ahead you are forecasting
Evaluate how valid your forecast is in context.
Choosing the best model relates to the forecast. Students need to work through the process of choosing a good model before they do the forecast from it. Then they need to justify what they have done. This is described in the next slide.
Does the forecast make sense?
What are the things that could make it completely wrong?

7. How well does your model follow the moving average trend line?
How well does your model follow the moving average trend line?
What is happening to the seasonal variation as the trend changes?
For how long do you think this model will be justified?
Who might find this forecast useful?
This was the best model from the previous presentation. Students need to look at the entire series as well as this graph to make comments.

8. Step 4: Seasonally adjusted data
Graph the actual (constant dollars), trend and seasonally adjusted data on the same graph.
The seasonally adjusted data helps you compare values from different seasons.
Calculate the % change between the quarters and comment
Suggested comments on this are given on the next few slides.

9. Calculate the % change between some of the more recent quarters.
Students will need to look at their own graph, though an enlarged version is given on the next slide. Calculating the % change from quarter to quarter is useful.
Calculate the % change between some of the more recent quarters.

10. Step 5: Improvements
Should you have used an additive or multiplicative method?
Justify your choice of model for the trend.
Were your results affected by outliers?
Improvements could also be justifying what was done. It is important that comments are specific and backed up by evidence from the data. Outliers are discussed in more detail in the next slide.

11. Outliers
The purpose of time series analysis is to try to smooth the data.
Extreme outliers can distort the estimation of trend and seasonal components.
Identifying any outliers and discussing the effects on other components is important in your report.
One of the processes in seasonal adjustment is to identify and remove (temporarily) extreme outliers. This is not required by this course but an understanding of the effect of outliers is useful.

12. There are now optional slides showing:
A process for identifying outliers.
The use of a multiplicative model.
These are in advance of the requirements of the standard. They are included for extension of students.
There is a link from the webpage to an information sheet which covers how seasonal adjustment is done at Statistics New Zealand. This includes dealing with outliers as well as the whole seasonal adjustment process. The page is called ‘Analysis of time series information’.

13. Now finish off your analysis and report on retail clothing sales.
A sample of a possible report is provided.

14. The End
A worked example answer based on this PowerPoint is available for you to check your answers

15. More on outliers Definitions:
An outlier can be defined as an element in the irregular which is 1.8 standard deviations or more from the mean.
An extreme outlier can be defined as one which is more than 2.8 standard deviations from the mean.
The limits for these definitions of outliers vary. Overseas 1.5 and 2.5 are often used. Because New Zealand is a small country with a volatile economy, these higher values are used.

16. Calculate the mean and standard deviation of the outliers.
(Notice that the values are scattered around zero.)
Then identify the values which are outliers by the definitions on the previous slide.
This, once again, is very simplified. However the basic idea is to look at values which are more extreme than the average value. See the information sheet mentioned before for a discussion of this process.

17. Three outliers have been found. None of them are extreme.
Look at the effect on the graphs of the trend and the seasonal factor. Can you see how these outliers have affected the graphs?
How many moving average values would be affected by the largest outlier?
If you were forecasting for the next December, what would be the effect of this outlier?
There should be ‘peaks’ (or troughs) in the lines on the graph corresponding to these points.
Affected moving average values would be any that contain the point with this outlier in it. They are likely to be higher that they should be.
The largest outlier is a December point. The forecast for next December would be higher than it should be as the seasonal adjustment value will be higher. The distortion in the trend may also affect the model used for the forecast.

18. Multiplicative analysis
Some series follow a multiplicative model where data values are found by:
actual = trend x seasonal x irregular
This means that where you would subtract in the analysis of an additive series you divide instead.
Open the worksheet marriage from examples.xls
Reminder: In a multiplicative series the amplitude of the seasonal factor increases or decreases with the trend.
The process is explained in detail in the next slides.

19. Marriage data Always begin by drawing the series.
This data has been slightly amended to make this more clear cut.
Always begin by drawing the series.
Does this qualify as multiplicative?

20. Notice this step!
The moving average calculation is unchanged. The first change is to divide by the moving average value instead of subtracting.

21. And this one.
Similarly for the seasonally adjusted value.

22. And this one!
Also for the irregular component.

23. The seasonally adjusted graph looks much as usual.

24. For September it is a lot less.
Notice:
The seasonal component is greater than 1 for December and March and June.
For September it is a lot less.
Look at the seasonal pattern on the graph on the previous slide.
The main difference is that the seasonal pattern is compared to one not to zero as in an additive model. The numbers are also much smaller. So a trough is a number between zero and one and a peak between one and two.

25. The irregular component has values scattered around 1.
In an additive series values would be scattered around zero.
Find any outliers.
Check them out on the graph.
The outliers look very small. However, an outlier of 1.2, for example, would be 20% higher than usual.

26. This is the actual end!
Haere rā ngā tauira mā!