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Temporal aggregation and seasonal adjustment

Due to user demand, the Australian Bureau of Statistics (ABS), in some instances, publishes original, seasonally adjusted and trend estimates at different observation frequencies for the same indicator. Hence sometimes at the quarterly level, original time series estimates are simply a temporal aggregate of their monthly counterpart. Suppose a time series of quarterly seasonally adjusted estimates is desired from such an equivalent time series pair. These estimates can be obtained via two approaches: either by (1) seasonally adjusting the quarterly original time series directly or by (2) seasonally adjusting the monthly original time series and then temporally aggregating to the quarterly level (referred to as the temporal aggregation approach hereafter). The ABS currently uses the first approach for seasonally adjusting equivalent time series pairs. This causes quality and consistency issues along with duplicate work.

The ABS knows from previous research that estimating calendar-related effects is more accurate when performed at the monthly level and then applied to the quarterly case. This idea of using a monthly time series to estimate a component of its quarterly equivalent is taken further by the temporal aggregation approach. The aim becomes to completely derive the quarterly seasonally adjusted series from its monthly seasonally adjusted counterpart. Hence significant improvements in quality and consistency are expected to be made.

For the Census X11 method, literature suggests that seasonal adjustment first and temporal aggregation second is the more efficient approach in terms of mean squared error and forecast performance. However, the impact of temporal aggregation on current end revisions had not been assessed for the mixed X11/ARIMA forecasting method utilised by the ABS.

The ABS hence conducted case studies to compare the quarterly seasonally adjusted estimates obtained via the two approaches using the ABS X11/ARIMA forecasting method, in terms of their relative efficiency, revisability and consistency. These included analyses on both simulated data and real ABS Balance of Payments estimates. The background, methodological basis and results from these studies were summarised and presented in an ABS Methodological Advisory Committee paper in June 2008 ("Temporal Aggregation and Seasonal Adjustment", cat. no. 1352.0.55.095). The conclusion from the paper was favourable for the temporal aggregation approach because this research indicated that consistency and productivity gains are made and that the quality of seasonal adjustment is not compromised. The ABS now plans to conduct further empirical studies to explore the temporal aggregation approach with ABS Agriculture Survey estimates where it is hoped a more diverse range of series can be explored along with the impact of sampling error effects.

For more information, please contact Lisa Apted on (03) 6222 5932 or lisa.apted@abs.gov.au, or Mark Zhang on (02) 6252 5132 or mark.zhang@abs.gov.au.