Multiplicative Decomposition: Dissection
(Using Average of All Data to Compute Seasonal Indexes)
I have prepared this handout to help you understand Multiplicative Decomposition, all steps
involved in it, and why it is important to account for seasons if time series has seasonality in it.
I hope you find it worthwhile.
Dr. J.
_______________________________________________
The bolded data in table 1 show a time series.
Table 1: 4Year Time series data, and its seasonal indexes
The following line graph shows the time series data with a linear trend line inserted in the line graph.
Clearly there is positive trend and also recurring seasonal effects in this time series. Therefore, we
must use a forecasting method that accounts for both.
The number of seasons in this data is 4, which represents Q1, Q2, Q3, and Q4. These are the
recurring seasons in each year.
Figure 1: Line graph of actual time series data (16 quarters)
1
Quarter
Year 1
Year 2
Year 3
Year 4
Total
1
218
225
234
250
1000
2
247
254
265
283
1033
3
243
255
264
289
1090
4
292
299
327
356
1178
Total
927
1049
1051
1274
4301
Qtr. Avg.
231.75
262.25
262.75
318.5
268.81
Seasonal
Indexes
0.8621
0.9756
0.9775
1.1849
Average of
all 16
quarters.
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To compute the seasonal indexes for the four quarters, since we have an even number of seasons
(i.e., 4 is an even number), you could use CMA (centered moving averages). Essentially, if the
number of seasons is even (like 12 months, or 4 quarters, etc.), then you could use CMA to compute
seasonal indexes.
You could use CMA b/c we have "even" numbered seasons. Since we have 4 quarters, and 4 is an
even number, you would use CMA. But CMA is a timeconsuming process for big data sets
if using
hand calculations
. Instead, I suggest using AVERAGING ALL DATA. By the way, the QM
software has options to perform both CMA and Average of All Data calculations when working with
seasonal data.
I have listed below the process for manual calculations when using Average of All Data. The steps
below show you how to compute the seasonal indexes, how to deseasonalize the data, and how to
create unadjusted and seasonallyadjusted forecasts.
_________________________________________________________
The manual process to do seasonal analysis is summarized below. To understand, you will need the
files that I have attached. The QM file uses Time Series, Multiplicative Decomposition, 4 seasons,
AVERAGE of ALL DATA.
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 Spring '08
 Nabavi
 Forecasting, Linear Regression, Regression Analysis, line graph, Time series analysis

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