DESESONALISING TIME SERIES
Unemployment figures have been collected over a 5-year period and presented in this table. It is difficult
to see any trends, other than seasonal ones.
a Calculate the seasonal indices.
b Deseasonalise the data using the seasonal indices.
c Plot the original and deseasonalised data.
d Comment on your results, supporting your statements with mathematical evidence.
Season
Summer
Autumn
Winter
Spring

2005
6.2
8.1
8.0
7.2
2006
6.5
7.9
8.2
7.7
2007
6.4
8.3
7.9
7.5
2008
6.7
8.5
8.2
7.7
2009
6.9
8.1
8.3
7.6
Note: Do all calculations to 4 d.p
CALCULATING SEASONAL INDICES
Step 1: Find the yearly averages over the four seasons for each year and put them in a table.
2005: (6.2 + 8.1 + 8.0 + 7.2) ÷ 4 = 7.3750
2006: (6.5 + 7.9 + 8.2 + 7.7) ÷ 4 = ______
2007: (6.4 + 8.3 + 7.9 + 7.5) ÷ 4 = ______
2008: (6.7 + 8.5 + 8.2 + 7.7) ÷ 4 = ______
2009: (6.9 + 8.1 + 8.3 + 7.6) ÷ 4 = ______
Year
Average
2005
2006
2007
2008
2009
7.3750
Step 2: Divide each term in the original time series by its yearly average.
Summer 2005: 6.2 ÷ 7.3750 = 0.8407
Autumn 2005: 8.1 ÷ 7.3750 = 1.0983
Winter 2005: 8.0 ÷ 7.3750 = 1.0847
Spring 2005: 7.2 ÷ 7.3750 = 0.9763
Summer 2006: 6.5 ÷ 7.5750 = 0.8581.
.
Spring 2009: 7.6 ÷ 7.7250 = 0.9838
Season
2005
2006
Summer
0.8407
0.8581
Autumn
1.0983
Winter
1.0847
Spring
0.9763
2007
2008
2009
0.9838
Step 3: Determine the seasonal averages from this second table. These are called seasonal indices.
Summer: (0.8407 + 0.8581 + 0.8505 + 0.8617 + 0.8932) ÷ 5 = 0.8608
Autumn: (1.0983 + 1.0429 + 1.1030 + 1.0932 + 1.0485) ÷ 5 = _______
Winter: (1.0847 + 1.0825 + 1.0498 + 1.0547 + 1.0744) ÷ 5 = _______
Spring: (0.9763 + 1.0165 + 0.9967 + 0.9904 + 0.9838) ÷ 5 = _______
Season
Summer
Seasonal index
0.8608
Autumn
Winter
Spring
DESEASONALISING THE DATA USING THE SEASONAL INDICES
Step 1: Divide each term in the original series by its seasonal index. This is the seasonally adjusted
or deseasonalised time series.
Note: Your answers may vary a little, depending upon how and when you rounded your calculations.
Summer 05: 6.2 ÷ 0.8608 = 7.2023
Autumn 05: 8.1 ÷ 1.0772 = 7.5195
.
.
.
Spring 09: 7.6 ÷ 0.9927 = 7.6557
2005
Summer
7.202
2006
2007
2008
2009
7.551
Autumn
Winter
Spring
7.656
PLOTTING THE ORIGINAL DATA AND DESEASONALISED DATA
There appears to be a slight upward trend in unemployment.