time series basics

8/6/2019 Time Series Basics

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September 2005 Created by Polly Stuart 1

Analysis of Time Series Data

For AS90641

Part 1

Basics for Beginners


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Contents This resource is designed to suggestsome ways students could meet therequirements of AS 90641.

It shows some common practices inNew Zealand schools and suggestsother simplified statistical methods.

The suggested methods do notnecessarily reflect practices of StatisticsNew Zealand.


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Aims

This presentation takes you through theprocess of analysing the data in an Excel

spreadsheet, drawing the graphs andidentifying the trend. It also shows you how todo a forecast.

You will need to open the spreadsheet:Example sales.xls

Choose the worksheet labelled Hardware.


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Time series data

Shows what happens as time passes.

Each data point is made up of3

components: Trend

Seasonal

Irregular.

For an additive series:

Data value = Trend + Seasonal +Irregular


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Beginnings

It is important to look at the series youare analysing before you start.

Draw a graph.

Look for the different components.

Think about what might be the best wayof analysing it.


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Look at: the trend

the seasonal component

the irregular

Ret il S les of e

100

150

200

250

00

Mar

1991

Mar

1992

Mar

199

Mar

1994

Mar

1995

Mar

1996

Mar

1997

Mar

1998

Mar

1999

Mar

2000

Mar

2001

Mar

2002

Mar

200

Quarter

$ illion

0


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Table

Use this to separate out all the

components of the series.


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Set up the column titles in the spreadsheet


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Step 1 is to identify the trend: Use a moving average to estimate a

trend.

Because it is quarterly data, use anorder of 4 initially.

Then centre the value by doing a

moving average order 2. In Excel you can do both columns in

one go (see the next slide).


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Click into the column next to the third datavalue (C9)

Click the button to open the function box

Choose AVERAGE or MEDIAN.

xf

Fill in the boxes by highlighting cells on your

spreadsheet.


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Rounding: Rounded to 3sf (why?).

Excel will use all the decimals in its calculations sorounding error is not a problem here.

Filldown

thecolumn.


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Delete the last 2 trend values. You dont haveenough information for those moving averages.

Colouring the cells helps to remind you not to use

them.


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Step 2 is to estimate the seasonalcomponent:

Subtract out the trend to leave theestimated seasonal and irregularcomponents.

Use a moving average to estimate the

seasonal component value.


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Calculate the seasonal and irregular values bysubtracting the trend estimate from the raw data

values, as shown below. You areremoving thetrend leavingthese two

components.This is calleddetrending!

Fill downthecolumn.


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Other methods for finding seasonalcomponents For short time series an average across

all the values for a season may be used

to find the seasonal effect. The moving average method is better

for longer series where the seasonal

pattern may be changing over the time. That is why we will use this method forthis data


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Calculate a moving

average over3 values ofthe seasonal and irregularcolumn for the quarter youwant. (September in thiscase as it is the firstquarter with a value in.)

[clickonthe firstthen hold

down Ctrltochoosetheothers]


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Fill down, then copy and paste (values only)the nearest 4 values into the spaces.

We are usingthe closestvalues as thebest estimate

of the missingones.

Do the samefor the bottom4 values.


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Calculate the seasonally adjusted values.

The seasonallyadjusted column

gives the values of

the trend and

irregular without the

seasons. It is useful to

compare the current

value with values

from previous

seasons


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Graphs


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Step 3 is to find a linear model for the

trend:

Be aware that the linear trend line givesa simplified estimation of the trend.

Fitting a straight line to the whole lengthof your moving average trend gives youa model to estimate its slope.

We look at other possible models in thePowerPoint Extra for Experts.


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Insert a new column at the start andput a count in it.

Filldown

pasttheend ofyour

table


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Highlight the next 3columns and click on

the graph icon to

draw the line graph .


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You can adjust itto look better ifyou want.

Re a Sa es ar are

100

150

200

250

3

M ar

1991

M ar

1992

M ar

199 3

M ar

1994

M ar

1995

M ar

1996

M ar

199 7

M ar

199 8

M ar

1999

M ar

2000

M ar

2001

M ar

2002

M ar

20 03

$

Hardw are

sales

rend

esti ate

0


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Estimating trend

This can be done in two ways

By looking at the moving average line atvarious points

By fitting a regression line. The first way gives a more accurate

estimate of the most recent trend.


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Method 1

Notice that from September 1998 the movingaverage rises steadily.

From the spreadsheet you can see that it rose $42million over the 4 years to September 2002.

So from September 1998 hardware sales rose byapproximately $10.5 million per year.

Retail Sales of Hardware

100

150

200

250

300

M ar

1991

M ar

1992

M ar

1993

M ar

1994

M ar

1995

M a r

199

M ar

1997

M ar

199 8

M ar

1999

M ar

2 0 0 0

M ar

2 0 0 1

M ar

2 0 0 2

M ar

2 0 0 3

$ million

ardw are

sales

rend

estimate

0


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Method 2

Get excel to put a linear regression lineon the data

This should be based on the moving

average line.

This will give an estimate for the wholeperiod of the series.

It may not be very accurate for the mostrecent values


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On the graph, right click on a trend estimatedata value and select Add trendline.

Make sure that Trend Estimate is highlighted inthe lower box. Click on options.

Choose the option to display the equation.


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The formula can be moved to be easier to see

Is the line a good model for forecasting termsin the series?

How could you do a better one?

R t il S l of H dw y 2

2

2

ar

ar

2

ar

ar

ar

ar

ar

ar

8

Mar

Mar

2

Mar

2

Mar

2

2

Mar

2

t

(m illion)

Hardware

sales

Trend

estimate

inear

Trendestimate

0


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Retail Sales of Hardware2

2

2

9 9

9 9 2

9 9

9 9

9 9!

9 9"

9 9#

9 9 8

9 9 9

2$ $ $

2$ $

2$ $

2

2$ $

Q u a r t e r

$ million

0

Identify the trend in context

The linear model for the trend line shows anincrease in hardware sales of $1.01 million perquarter. This is approximately $4 million per year.


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Step 4 is to calculate your forecast:

Use the formula from your model of thetrend line.

This gives an estimate of the trendcomponent.

Add back the seasonal component.

We will do an estimate for March 2004.


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To forecast forMarch 2004

Makesure thecountgoesdown tothequarteryou want

toforecastfor.


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Use the formulafrom your trendline to calculatethe estimatedtrend value for

March.


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Add back the seasonal effects for March using

the most recent March value.


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Forecast

In March 2004 the forecasted value for Retail Hardwaresales using this model is $219 million (3s.f). This is

calculated by substituting the number of periods sinceMarch 1991 into the formula for the trend. Then theseasonal adjustment for March is added back in.

Forecast = 1.0125 x 53 + 167.51 -2.47

BUT: youneed to be aware that your line did not followthe trend estimates very closely at the end.

The next presentation looks at some ways of makingbetter models.

50 Jun 2003

51 Sep 2003

52 Dec 2003

53 Mar 2004 218.71 221.1725


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A worked example of the report you

could produce for ales of RetailHardware is available for you tocheck

your results.


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The EndBut see Extra for Experts!

time series basics

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