1. Smoothing by moving average

2. 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

3. 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

4. Moving Average Method - Example

5. Three-year and Five-Year Moving Averages

6. 3-month Simple Moving Average
ORDERS
MONTH PER MONTH
MOVING
AVERAGE
Jan 120
Feb 90
Mar 100
Apr 75
May 110
June 50
July 75
Aug 130
Sept 110
Oct 90
Nov - –
103.3
88.3
95.0
78.3
85.0
105.0
110.0
MA3 = 3
i = 1  Di =
= 110 orders
for Nov
Concentrates on most recent data. The more dynamic the environment, the smaller n is used.
If we use n=2 (110+90) / 2 = 100
If we use n=4 ( ) /4 = 101,3
The n is established through trial and error.
Note: April’s forecast was way too high but the low sales corrected May’s forecast.

7. Moving Averages Example: Four-quarter moving average First average:
(continued)
Example: Four-quarter moving average
First average:
Second average:
etc…

8. Seasonal Data … … Quarter Sales 1 2 3 4 5 6 7 8 9 10 11 etc… 23 40 2527 32 48 33 37 50 … …

9. Calculating Moving Averages
Average Period
4-Quarter Moving Average
2.5
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
Quarter
Sales 1 23 2 40 3 25 4 27 5 32 6 48 7 33 8 37 9 10 50 11
etc…
Each moving average is for a consecutive block of 4 quarters

10. 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

11. Excel/Data Analysis/Moving Average