Seasonal component (for time-series data)

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

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)