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Time-series data which have had the seasonal component removed. In seasonally adjusted data the effect of regular seasonal phenomena has been removed.
In terms of an additive model for time-series data, Y = T + S + C + I, where
T represents the trend component,
S represents the seasonal component,
C represents the cyclical component, and
I represents the irregular component;
the smoothed series = T + C and
the seasonally adjusted series = T + C + I.
Example
Statistics New Zealand’s Economic Survey of Manufacturing provided the following data on actual operating income for the manufacturing sector in New Zealand. Centred moving means have been calculated. For the quarters with centred moving means the individual seasonal effect is calculated by:
Operating income (raw data) – (centred) moving mean
The overall seasonal effect for each quarter is estimated by averaging the individual seasonal effects. The two individual seasonal effects for March quarters are –588.125 and –561.75. The mean of these 2 values is –574.938. The other estimated overall seasonal effects are shown in the second table below.
Seasonally adjusted data is calculated by:
Operating income (raw data) – estimated overall seasonal effect
The calculation for the Mar-05 quarter is 17322 – (–574.938) = 17896.938
| Quarter | Operating income ($millions) |
Centred moving mean ($millions) |
Individual seasonal effect |
Seasonally adjusted ($millions) |
| Mar-05 Jun-05 Sep-05 Dec-05 Mar-06 Jun-06 Sep-06 Dec-06 Mar-07 Jun-07 Sep-07 Dec-07 |
17322 17696 17060 18046 17460 19034 18245 18866 18174 19464 18633 20616 |
17548.250 17732.750 18048.125 18298.750 18490.500 18633.500 18735.750 19003.000 |
-488.250 313.250 -588.125 735.250 -245.500 232.500 -561.750 461.000 |
17896.938 17097.875 17426.875 17773.125 18034.938 18435.875 18611.875 18593.125 18748.938 18865.875 18999.875 20343.125 |
The raw data and the seasonally adjusted data are displayed below. Note that M, J, S and D indicate quarter years ending in March, June, September and December respectively.
Curriculum achievement objectives reference
Statistical investigation: (Level 8)
