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Smoothing by moving average
0
10
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40
50
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1 2 3 4 5 6 7 8 9 10Quarter
Sale
s
Sales Smoothed
The Moving Average Method
Useful in smoothing time series to see its trend Basic method used in measuring seasonal
fluctuation Applicable when time series follows fairly linear
trend that have definite rhythmic pattern
Moving Averages
Used for smoothing Series of arithmetic means over time Result dependent upon length of period
chosen for computing means To smooth out seasonal variation, the
number of periods should be equal to the number of seasons For quarterly data, number of periods = 4 For monthly data, number of periods = 12
Moving Average Method - Example
Three-year and Five-Year Moving Averages
3-month Simple Moving Average
JanJan 120120
FebFeb 9090
MarMar 100100
AprApr 7575
MayMay 110110
JuneJune 5050
JulyJuly 7575
AugAug 130130
SeptSept 110110
OctOct 9090NovNov --
ORDERSORDERS
MONTHMONTH PER PER MONTHMONTH
MAMA33 = =
33
ii = 1= 1 DDii
33
==90 + 110 + 13090 + 110 + 13033
= 110 orders= 110 ordersfor Novfor Nov
––––––
103.3103.388.388.395.095.078.378.378.378.385.085.0
105.0105.0110.0110.0
MOVING MOVING AVERAGEAVERAGE
Moving Averages
Example: Four-quarter moving average
First average:
Second average:
etc…
(continued)
4Q4Q3Q2Q1average Moving 1
4Q5Q4Q3Q2average Moving 2
Seasonal Data
Quarter Sales
1234567891011
etc…
2340252732483337375040
etc…
Quarterly Sales
0
10
20
30
40
50
60
1 2 3 4 5 6 7 8 9 10 11
Quarter
Sale
s…
…
Calculating Moving Averages
Each moving average is for a consecutive block of 4 quarters
Quarter Sales1 23
2 40
3 25
4 27
5 32
6 48
7 33
8 37
9 37
10 50
11 40
Average Period
4-Quarter Moving
Average2.5 28.75
3.5 31.00
4.5 33.00
5.5 35.00
6.5 37.50
7.5 38.75
8.5 39.25
9.5 41.00
443212.5
42725402328.75
etc…
Fools forecaster by appearing to identify a cycle when in fact no cycle was present in the actual data
Any moving average is serially correlated as a number of periods have been averaged
Excel/Data Analysis/Moving Average