Upcoming SlideShare
×

Analysis of time series

3,017 views

Published on

Published in: Technology, Economy & Finance
0 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

• Be the first to like this

Views
Total views
3,017
On SlideShare
0
From Embeds
0
Number of Embeds
5
Actions
Shares
0
148
0
Likes
0
Embeds 0
No embeds

No notes for slide

Analysis of time series

1. 1. Analysis of Time Series For AS90641 Part 2 Extra for ExpertsSeptember 2005 Created by Polly Stuart 1
2. 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. 2
3. 3. 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. 3
4. 4. 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. 4
5. 5. Look at : the trend the seasonal component the irregular component C l o t hi ng and so f t g o o d s sal es \$(million) 550 500 450 400 350 300 2500 Mar Mar Mar Mar Mar Mar Mar Mar Mar Mar Mar Mar Mar 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 5
6. 6. Step 1: Using IndexesIndexes show how prices have changed over time.They show the percentage increase in prices sincea base period. The index for the base period isusually 1000.An index of 1150 shows that prices have increased15 percent since the base period.You can use indexes to ‘deflate’ time series datawhich contains dollar values.Statistics New Zealand indexes include:Consumers Price Index Labour Cost IndexFood Price Index Farm Expenses Price Index 6
7. 7. 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? 7
8. 8. If the value of sales from clothing shops areincreasing over time there several possiblereasons: • 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 increasingbecause of inflation we can turn the sales intoconstant 1999 dollars using the value of the CPIfor each year. 8
9. 9. Constant dollarsThe present base period for the ConsumersPrice Index (CPI) is 1999.Assume that the CPI now is 1150. In 1999, \$100 could buy the same amount as: 1150 100 \$115 can buy now 1000 Now, \$100 can buy the same amount as: 1000 100 \$86.96 could buy in 1999 1150 9
10. 10. Calculate your deflated value We will use constant 1999 dollars Use this for the formula to rest of calculate this the value in exercise. constant 1999 dollars. 10
11. 11. Step 2: Deciding on an appropriatemodel • 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 11
12. 12. AdditiveWhen the size of the Series for which an additive series isseasonal appropriate 250component stays 200about the same as 150the trend changes, 100then an additive 50 0method is usually Mar 1991 Mar 1992 Mar 1993 Mar 1994best. Original series Trend series 12
13. 13. Multiplicative Series for which a multiplicative model is appropriateWhen the size of 300the seasonal 250component 200 150increases as the 100trend increases, 50then a 0 Mar 1991 Mar 1992 Mar 1993 Mar 1994multiplicative Original seriesmethod may be Trend seriesbetter. 13
14. 14. 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). C l o t hi ng a nd s o f t g o o d s r e t a i l t r a d e \$million 550 500 450 400 350 300 250 0Mar Mar Mar Mar Mar Mar Mar Mar Mar Mar Mar Mar Mar 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 14
15. 15. 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. 15