Minister of Finance

Instructor: Le Thi Ngoc Tu Group members: Tran Tien Manh

Pham Thi Huyen Ly Thi Thuy Linh

Nguyen Van Hiep

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Recall Regression ModelX: independent variableY: dependent variable Time-series:- Definition: Variable measured over time in sequential order

- Independent variable: Time

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Example:

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+ Long-term trend: Smooth pattern with duration > 1 year

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+ Cyclical effect: wavelike pattern about a long-term trend, duration > 1 year, usually irregular

Cycles are sequences of points above

& below the trend line

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+ Seasonal effect: like cycles but short repetitive periods, duration < 1 year (days, weeks, months…)

Sales peak in Dec.

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+ Random variation: irregular changes that we want to remove to detect other components

Time

Random variation

that does not

repeat

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Purpose: Remove random fluctuation

to detect seasonal pattern

2 types:

- Moving average (MA)

- Exponential smoothing

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Example of Moving average:

Period t yt3-period

MA4-period

MA4-period centred

MA

1 12 - - -

2 18 15.33 - -

3 16 19.33 17.5 18.13

4 24 19.00 18.75 18.50

5 17 19.00 18.25 19.38

6 16 19.33 20.5 20.13

7 25 20.67 19.75 -

8 21 - - -13

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Measuring seasonal effect

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Values of St x Rt

  Quarter  

Year 1 2 3 4 Total

2005 - - 1.0239 1.0254  

2006 0.9918 0.9572 1.0281 1.0318  

2007 0.9869 0.9548 1.0316 1.0212  

2008 1.0012 0.9592 1.0134 1.0481  

2009 0.9900 0.9304 - -  

Average (Si) 0.9925 0.9504 1.0242 1.0316 3.9987

Seasonal Index (Si) 0.9928 0.9507 1.0246 1.0319 4.0000

Forecast of trend & seasonality:

Ft = [ β0 + β1t ] SIt

where:

Ft = forecast for period t

SIt = seasonal index for period t

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Year Month CPI2005 1 101.1

2 102.53 100.14 100.65 100.56 100.47 100.48 100.49 100.810 100.411 100.412 100.8

2006 … …… …

2008 48 99.3

Using the following data

about CPI of Viet Namfrom 2005 to 2008 forforecasting CPI in 2010:

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Reasons:

- CPI is measured over time (monthly)

- 3 components exist

Technique: Time-series forecasting with

regression

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Random variation

in 2008

CPI peaks in

Feb

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Trend analysis Using Excel, the trend line is:

yt = 100.551 + 0.016 t

y = 100.551 + 0.016 t

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Measuring seasonal effect

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Seasonal index

Apply the formula: Ft = [ β0 + β1t ] SIt

Month 1 2 3 4 5 6

SI t 1.0055 1.017 0.997 0.9998 1.0055 1.0005

Month 7 8 9 10 11 12

SI t 0.9975 0.9975 0.9945 0.9928 0.9935 0.9988

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Forecast CPI in 2008

Forecast CPI of 2008 did not match actual CPI due to unexpected events (recession)

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Forecast CPI in 2010

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- Long term trend: slight increase in CPI

- Seasonal effect: peak in Feb.

y = 100.551 + 0.016 t

Forecasted

CPI

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‘Time Series Analysis’, Citing or referencing electronic sources of information, viewed 15 May 2010, http://www.statsoft.com/textbook/time-series-analysis/?button=3

Australian Bureau of Statistics, ‘Time Series Analysis: The Basics’, viewed 15 May 2010, http://www.abs.gov.au/websitedbs/d3310114.nsf/4a256353001af3ed4b2562bb00121564/b81ecff00cd36415ca256ce10017de2f!OpenDocument#WHAT%20IS%20A%20TIME%20SERIES%3F

‘Introduction to Time Series Analysis’, Citing or referencing electronic sources of information, viewed 15 May 2010, http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc4.htm

Berenson, M. & Levine, D. 1998, Business Statistics - A first course, Prentice Hall Press.

Anderson, D., Sweeney, D. & Williams, T. 1999, Statistics for business and economics, South-Western College Publishing, Ohio.

Selvanathan, A., Selvanathan, S., Keller, G. & Warrack, B. 2004, Australian business statistics, Nelson Australia Pty Limited.

 

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