Use of ARIMA Modelling to Improve Seasonally Adjusted Estimates
The Australian Bureau of Statistics (ABS) publishes seasonally adjusted and trend estimates which are calculated from original estimates using the ABS seasonal adjustment package, SEASABS.
The original estimates comprise seasonal, trend and irregular. The seasonal component represents the systematic and calendar related effects, the trend component represents the underlying direction in the series, and the irregular component is the remaining component of the series after the seasonal and trend components have been removed. Seasonally adjusted estimates are calculated by estimating and removing the systematic and calendar related effects from the original estimates. The trend is calculated by smoothing the seasonally adjusted estimates. Both seasonally adjusted and trend estimates need the unknown future data to achieve good estimation properties.
Both estimates are subject to revision at the current end of a series once additional observations become available or the original estimates are revised. An objective is to achieve accurate seasonally adjusted and trend estimates with small revisions at the current end of the series. This can be achieved using an Integrated Autoregressive Moving Average (ARIMA) modelling approach.
This will be implemented for the Monthly Retail Trade series (ABS Catalogue 8501.0) from August 2004. This method will be progressively introduced to other ABS time series as appropriate.
The current ABS seasonal adjustment approach, SEASABS, uses moving averages which are a set of weights of a given length designed to extract specific information from the data. As part of intermediate calculations in the seasonal adjustment process, the moving averages require data points to be available either side of the point of interest. At the end of a time series, assumptions are made about the data points that extend beyond the source series observations. These assumptions are built into the design of the asymmetric moving average weights used in the seasonal and trend moving averages. ARIMA modelling is a technique that can be used to extend estimates at the end of a series. The use of these techniques generally results in a reduction in revisions to data when subsequent observations become available.
The data points projected by the ARIMA model are temporary intermediate values that are only used to improve the estimation of the seasonal factors. The projected data do not affect the original estimates and are discarded at the end of the seasonal adjustment process.
Previous work (see references below) has evaluated ARIMA modelling against 820 series across 11 subject matters. It highlighted a reduction in the size of the revisions to seasonally adjusted estimates in the order of 7.7%. While ARIMA modelling on average reduces the revisions for each subject matter area, there can be individual series where the technique actually increases the size of the revisions. However, the overall average improvement and the sound theoretical underpinnings outweigh the chance of increased revisions in most series.
More details on the implementation of ARIMA models as part of the ABS seasonal adjustment process can be obtained in a forth coming issue of Australian Economic Indicators, Catalogue number 1350.0, or the Methodology Advisory Committee paper 'Use of ARIMA Models for Improving Revisions of X-11 Seasonal Adjustment', November 2001, available from www.abs.gov.au.
For more information, please contact Craig McLaren on (02) 6252 6540
Email: craig.mclaren@abs.gov.au or
Mark Zhang on (02) 6252 5132.
Email: mark.zhang@abs.gov.au
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