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Use of Power Transformations in Seasonal Adjustment

In the ABS, seasonal adjustment of a time series is performed by first specifying an appropriate decomposition model. It is desirable to choose a decomposition model such that stable seasonal factors can be obtained. Common candidates for decomposition in the ABS include the multiplicative and additive models, where the seasonal factors are constrained to average out to unity and zero respectively. Currently, the ABS is considering the use of Box-Cox models, which are a family of power transformations encompassing both the multiplicative and additive options. It is well established in literature that appropriate Box-Cox transformation of data can correct for heteroscedastic and non-normal residuals, and in the setting of seasonal adjustment of time series, this can potentially lead to more stable seasonal factor estimates.

The ABS has hence conducted preliminary studies on some volatile overseas arrivals and departures series which suggest the use of Box-Cox transformation as being advantageous over the multiplicative adjustment. This was based on a revisions analysis, in that the application of a power transformation resulted in reduced current end revisions to the concurrent seasonally adjusted series. Such results have motivated further studies, in that the ABS is now investigating when power transformations should be used, how they should be used, and of course, their performance against the original adjustment. This performance will be assessed using quality measures such as significance tests for residual seasonality, summary statistics for the stability of seasonal factors and revisions to concurrent seasonally adjusted estimates. Some existing methods in regards to selecting the power transform parameter are being examined, including that of maximum likelihood estimation and a time series variance stabilisation method. Results from these approaches will then be compared to those of when a simple grid search of the transform parameter is performed. The ABS is working towards presenting the findings in the Methodology Advisory Committee paper to be submitted and reviewed in June this year.

For more information on this project, please contact Leanne Chhay on (02) 9268 4720 or leanne.chhay@abs.gov.au or Alex Stuckey on (08) 9360 5378 or alex.stuckey@abs.gov.au.