smoothing by moving average

Smoothing by moving average

0

10

20

30

40

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60

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