Seasonally adjusted chain-linked volume estimates

6.54    The compilation of seasonally (and calendar) adjusted quarterly chain-linked volume measures is the result of a sequence of operations, including seasonal and calendar adjustment, partial balancing, chain-linking and benchmarking. It is somewhat more complicated than deriving chain-linked original estimates because some of these steps need to be undertaken on unlinked data (partial balancing) and some need to be undertaken on chain-linked data (benchmarking, and seasonal and calendar factor estimation). The objective is to achieve the following for the seasonally adjusted chain linked data:

• they should be of sufficiently high quality, with no residual seasonality and no over-adjustment (the seasonal component should not contain irregular influences);
• when expressed in the average prices of the previous year they should be additively consistent, preferably with no statistical discrepancies; and
• they should be temporally consistent with the same annual chain volume benchmarks used for the original data.³⁵ 

6.55    The following paragraph describes the steps taken in deriving seasonally adjusted, partially balanced and benchmarked, chain-linked quarterly Australian national accounts data:

1. Seasonally analyse each chain-linked quarterly national account series at the lowest level of aggregation at which seasonal adjustment is undertaken to derive seasonal and calendar adjustment factors.
2. Derive seasonally adjusted estimates in the average prices of the previous year. If the multiplicative model is used, then the factors can be applied directly to original data in the prices of the previous year (see Chapter 7 for detail on the multiplicative model). If any other model is used the seasonally adjusted chain-linked series needs to be unlinked.

3. Aggregate the data to derive seasonally adjusted estimates in the average prices of the previous year for all major aggregates.

4. Partially balance the accounts in a S-U framework.

5. Chain link the estimates.

6. Benchmark the chain-linked, seasonally adjusted volume estimates to the corresponding annual data.

7. Run all the benchmarked series through the seasonal adjustment diagnostics to check for residual seasonality or any other problems. If there are any, go back to step 1 and recalculate the seasonal factors using the balanced and benchmarked original data.