minister of finance instructor: le thi ngoc tu group members: tran tien manh pham thi huyen ly thi...
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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
Time9
+ 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
=
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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