chapter 6 - time series analysis.pdf
TRANSCRIPT
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QMT412 Pn. Sanizah's Notes 03/05/201
COMPONENTS OF
TIMES SERIES
TREND
(T)
HistogramMethod of
LeastSquares
MovingAverage
CYCLICALVARIATIONS
(C)
SEASONALVARIATIONS
(S)
AdditiveModel
MultiplicativeModel
IRREGULARVARIATIONS
(I)
COMPONENTS OF A TIME SERIES (1)TREND
long termgeneral movement where thevalue of the variable tends to increase or
decrease over a long period of time (morethan10 years).
Example : Cost of living reflect the Consumer PriceIndex (CPI)
(2) CYCLICAL VARIATIONS
movement repeats its patterns over a periodof time (2-10 years)
Example : Economic recession
Cont (3) SEASONAL VARIATION
involve pattern of change which arerepeated from year to year.
Example : weather and holidays
(4) IRREGULAR VARIATIONSdescribe the movements of variable whichis completely unpredictable
Example : earthquake, tsunami, epidemics
COMPONENT OF A TIME SERIES
TREND ANALYSIS Trend can be described using a graph called histogram
where the independent variable (x-axis) is timeanddependent variable (y-axis) is the observedvariable.
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QMT412 Pn. Sanizah's Notes 03/05/201
Example 2 (pg. 170) The following table shows the sales of an electrical item of a
company for the year 2009 to 2011.
a) Plot the data.
b) Calculate the trend using the least squares method.
c) Estimate the trend values for 1stand 2ndquarter 2009.
d) Forecast the trend of sales for 1 stand 2ndquarter 2012.
Year
Sales (RM000)
1stQuarter 2ndQuarter 3rdQuarter 4thQuarter
2009 48 44 26 382010 65 32 30 35
2011 73 38 34 46
(2) Moving Average Method
Calculated by averaging the most recent
nvalues in a time series
Can be used to forecast the data value for the next
period but not for periods which are too far in thefuture
Centred moving average
(when the period is an even number of terms)
i.e.: monthly (12), quarterly (4)
Simple moving average
(when the period is an oddnumber of terms)
i.e.: 5 days a week, three (3) shifts a [email protected]
Example 3 (pg. 172)The following table shows the sales of an electric
company for the year 2009 to 2011.
a) Calculate the trend values using the movingaverage method.
b) Forecast/estimate the trend values for 1stand 2ndquarters of the year 2012.
YearSales (RM000)
1stquarter 2ndquarter 3rdquarter 4thquarter
2009 48 44 26 38
2010 65 32 30 35
2011 73 38 34 46
Example 4 (pg. 174)
Table shows the number of computers produced by afactory during the morning, afternoon and eveningshifts of the week.
Calculate the trend values using the moving averagemethod.
Day Morning (M) Afternoon (A) Evening (E)
Monday 255 224 241
Tuesday 234 239 250
Wednesday 237 233 256
Thursday 240 227 259
Friday 240 230 256
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QMT412 Pn. Sanizah's Notes 03/05/201
COMPONENT OF A TIME SERIES
SEASONALVARIATIONS
ADDITIVEMODEL
MULTIPLICATIVEMODEL
We will onlydiscuss on
multiplicativemodel
Seasonal VariationMultiplicative model
Actual data = trend xseasonal variation
xcyclical variation xcatastrophic variation
xresidual variation
Let the assumption be:
There is NO cyclical or catastrophic component
Then the formula is:
Actual data=trend x seasonal variation x residual variation
Example 5 (Pg. 177)Table shows the sales of an electrical item of acompany for the year 2009 to 2011.
(a) Calculate the seasonal index of the sales for each
quarter and interpret the results.
(b) Forecast the sales for the 1stand 2ndquarters of
the year 2012.