Transcript Reporting.ppt

Analysis of Time Series
For AS90641
Part 3
Reporting
September 2005
Created by Polly Stuart
1
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.
2
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
3
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.
4
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
Display your graphs as evidence for your comments.
Be specific, think about the context.
5
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.
Does the forecast make sense?
What are the things that could make it completely
wrong?
6
Clothing and softgoods sales from 1998
y = 4.3368x + 335.87
$(million)
500
450
400
350
300
2500
Mar
1998
Clothing
1999
dollars
Estimated
trend
Mar
1999
Mar
2000
Mar
2001
Mar
2002
Mar
2003
Linear
(Estimated
trend)
• 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?
7
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
8
C l ot hi ng a nd sof t goods sa l e s
$ ( mi l l i o n )
500
Cl othi ng
450
1999
400
dol l ar s
350
Esti mated
tr end
300
2500
M ar M ar
Seasonal l y
M ar M ar M ar M ar
M ar M ar M ar M ar
M ar M ar M ar
adj usted
1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003
Calculate the % change between some of the more recent
quarters.
9
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?
10
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.
11
There are now optional slides
showing:
• A process for identifying outliers.
• The use of a multiplicative model.
12
Now finish off your analysis
and report on retail clothing
sales.
13
The End
A worked example answer based on this
PowerPoint is available for you to check your
answers
14
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.
15
• 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.
16
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?
17
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
18
Marriage data
Number of Marriages Registered
10,000
8,000
6,000
4,000
2,000
0
Mar Mar Mar Mar Mar Mar Mar Mar Mar Mar Mar Mar Mar Mar
1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972
Always begin by drawing the series.
Does this qualify as multiplicative?
19
Notice this step!
20
And this
one.
21
And this
one!
22
Number of marriages registered
10000
Number of
marriages
8000
Estimated
trend
6000
4000
Seasonally
adjusted
2000
0
M ar M ar M ar M ar M ar M ar M ar M ar M ar M ar M ar M ar M ar M ar
1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972
23
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.
24
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.
25
This is the actual end!
Haere rā ngā tauira mā!
26