Time-series Analysis Forecasting 03
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MinisterofFinance
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Introduction
OverviewComponents of time series
Analysis
Smoothing techniques
Trend analysis
Measuring seasonal effect
Forecasting
Time-series forecasting with regression
Application
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Recall Regression Model: independent variable
: dependent variable
Time-series:- Definition: Variable measured overtime in sequential order
- Independent variable: Time
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Example:
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Long-term
trend
(T)
Cyclical
effect
(C)
Seasonal
effect
(S)
Random
variation
(R)
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+ Long-term trend: Smooth pattern withduration > 1 year
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+ Cyclical effect: wavelike pattern about along-term trend, duration > 1 year, usuallyirregular
Cyclesaresequencesofpointsabove & belowthe trendline
Time
Volu
me
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+ Random variation: irregular changes that wewant to remove to detect other components
Time
Volum
e
Random
variation that
does not repeat
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Example ofMovingaverage:
Period
t yt
3-period
MA
4-period
MA
4-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 -
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Trend analysis
Techniques
Linear model:
yt = 0 + 1t +
Polinomial
model
Purpose Isolate thelong-term trend
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Forecast of trend & seasonality:
Ft
= [ 0
+ 1
t ] SIt
where:
Ft = forecast for period t
SIt = seasonal index for period t
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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 2008CPI 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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Calculate MAt: Mulplicative model:
yt= Ttx Ct x St x Rt
MAt= Tt x Ct
Yt Ttx Ct x St x Rt
MAt Tt x Ct
Calculate average of St x RtS
t
St is adjusted SIt, so that
average SIt= 1
Measuring seasonal effect
=
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Forecast CPI in 2010
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- Long term trend:slightincreaseinCPI
-Seasonal effect: peak inFeb.
y = 100.551 + 0.016 t
Forecasted
CPI
