September 2005 Created by Polly Stuart 1 Analysis of Time Series For AS90641 Part 2 Extra for Experts
Jan 08, 2016
September 2005 Created by Polly Stuart 1
Analysis of Time Series
For AS90641
Part 2 Extra for Experts
2
Contents• This resource is designed to suggest
some ways students could meet the requirements of AS 90641.
• It shows some common practices in New Zealand schools and suggests other simplified statistical methods.
• The suggested methods do not necessarily reflect practices of Statistics New Zealand.
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Aims• This presentation (and the next) takes
you through some extra types of analysis you could try for time series data.
• It also makes suggestions for writing your report
• You will need to open the spreadsheet: Example sales.xls
• Choose the worksheet labeled Clothing.
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Beginnings• You have already learned a basic
analysis of a time series and how to isolate some components.
• We are now going to do a more complex analysis.
• Before doing any analysis you need to:– Graph the raw data– Identify the components of the data– Decide on the best method of analysis.
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Look at : the trend
the seasonal component
the irregular component
Clothing and softgoods sales
250
300
350
400
450
500
550
Mar
1991
Mar
1992
Mar
1993
Mar
1994
Mar
1995
Mar
1996
Mar
1997
Mar
1998
Mar
1999
Mar
2000
Mar
2001
Mar
2002
Mar
2003
0
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Step 1: Using Indexes Indexes show how prices have changed over time. They show the percentage increase in prices since a base period. The index for the base period is usually 1000.
An index of 1150 shows that prices have increased 15 percent since the base period.
You can use indexes to ‘deflate’ time series data which contains dollar values.
Statistics New Zealand indexes include:
Consumers Price Index Labour Cost Index
Food Price Index Farm Expenses Price Index
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Consumers Price Index• The Consumers Price Index (CPI) measures
the change in prices of a specific basket of goods and services in New Zealand.
• For retail sales of clothing this is an appropriate index to use as clothing is included in the ‘basket’ of goods priced.
• Open the CPI worksheet and copy the series into the next column of the clothing worksheet.
Look at the CPI data. Which is the base period? How do you know?
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If the value of sales from clothing shops are increasing over time there several possible reasons:
• Prices have increased because of inflation• The number of people in the population is growing
so there are more possible customers needing clothes
• Sales are actually increasing because people are buying more clothing
• Something else?
To help find out if total sales are increasing because of inflation we can turn the sales into constant 1999 dollars using the value of the CPI for each year.
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Constant dollars
115$1001000
1150
The present base period for the Consumers Price Index (CPI) is 1999.
Assume that the CPI now is 1150.
Now, $100 can buy the same amount as:
96.86$1001150
1000
can buy now
could buy in 1999
In 1999, $100 could buy the same amount as:
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We will use constant 1999 dollars for the rest of this exercise.
Use this formula to calculate the value in constant 1999 dollars.
Calculate your deflated value
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Step 2: Deciding on an appropriate model
• Some data follows an additive model where:
Data value = trend + seasonal + irregular• Other data follows a multiplicative
model where:
Data value = trend x seasonal x irregular
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Additive
When the size of the seasonal component stays about the same as the trend changes, then an additive method is usually best.
Series for which an additive series is appropriate
0
50
100
150
200
250
Mar 1991 Mar 1992 Mar 1993 Mar 1994
Original series
Trend series
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When the size of the seasonal component increases as the trend increases, then a multiplicative method may be better.
Multiplicative
Series for which a multiplicative model is appropriate
0
50
100
150
200
250
300
Mar 1991 Mar 1992 Mar 1993 Mar 1994
Original series
Trend series
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Look again at the graph below• Which model seems more suitable?
In the previous PowerPoint we used an additive model and we will do this also for this data
(An example of using a multiplicative model is given at the end of the third presentation).
Clothing and softgoods retail trade
250300350400450500550
Mar
1991
Mar
1992
Mar
1993
Mar
1994
Mar
1995
Mar
1996
Mar
1997
Mar
1998
Mar
1999
Mar
2000
Mar
2001
Mar
2002
Mar
2003
0
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Step 3: Analyse the data
• Do the spreadsheet analysis as far as calculating the seasonally adjusted data.
• Use the constant dollar values for your analysis.
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Your spreadsheet should look like this:
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Step 4: Describe and justify your model for the trend
• Try some different models for the moving average.
• Decide which one will give a sensible forecast.
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Trend
Does this linear trend model look sensible?
Describe what you can see.
Clothing and softgoods salesy = -0.0864x + 381.6
250
300
350
400
450
500
Mar1991
Mar1993
Mar1995
Mar1997
Mar1999
Mar2001
Mar2003
$(million)
Clothing1999dollarsEstimatedtrend
Linear(Estimatedtrend)
0
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• Many trends cannot be modelled by a single straight line
• A quadratic model may be tempting…
But is it realistic?
Clothing and softgoods salesy = 0.1097x2 - 5.572x + 431.66
250
300
350
400
450
500
Mar1991
Mar1993
Mar1995
Mar1997
Mar1999
Mar2001
Mar2003
$(million)
Clothing1999dollarsEstimatedtrend
Poly.(Estimatedtrend)
0
20
• Remember the shape of a parabola.• Do you think that sales (in constant dollars)
are going to grow at that rate?
Clothing and softgoods salesy = 0.1097x2 - 5.572x + 431.66
250300350400450500550600
Mar1991
Mar1993
Mar1995
Mar1997
Mar1999
Mar2001
Mar2003
$(million)
Clothing1999dollarsEstimatedtrend
Poly.(Estimatedtrend)
0
21
• An option is to use a linear model over the trend at the end of the series.
• This is likely to give the most realistic forecast.
Clothing and softgoods sales from 1998y = 4.3368x + 335.87
250300350
400450500
Mar1998
Mar1999
Mar2000
Mar2001
Mar2002
Mar2003
$(million)Clothing1999dollars
Estimatedtrend
Linear(Estimatedtrend)
0
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Step 5: Describing the seasonal component• A graph can help you to see the patterns more
clearly.
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Describe the patterns you can see.
You can also identify amounts easily from the graph.
Seasonal sales patterns
-50
0
50
Mar 1991 Mar 1995 Mar 1999 Mar 2003
$(million)
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Step 6: Analysing the irregular component• There is always random variation in a time
series, the irregular component.• When a very unusual event happens it may
cause a spike in the data, called an outlier.• This can distort the trend and seasonal
component values. • The larger the spike the more distortion. • It is useful to calculate the irregular
component and look for outliers.
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Subtract the values in the ‘Seasonal’ column from the ‘Seasonal and Irregular’ column. A graph is often useful.
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Outliers
Both the pattern of the irregular component and any extreme values are worth commenting on.
Irregular Component
-10
-5
0
5
10
15
Mar 1991 Mar 1995 Mar 1999 Mar 2003
$million 1999
Highlight the date and irregular columns for the graph.
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This is not the end!
Continue the analysis and write a report on retail
clothing sales.
Some ideas are given in the next presentation,
Reporting.