29.12. Choice of seasonal adjustment approach. TRAMO-SEATS and X-12-ARIMA are currently the most commonly used seasonal adjustment approaches. TRAMO-SEATS is based on a parametric approach (where the model structure is specified a priori), while X-12-ARIMA is based on a non-parametric approach (where the model structure is determined from the data). A third possible approach is to use structural time-series models, provided that they allow for a complete calendar and outlier treatment and include an adequate set of diagnostics. The consistent use of a common set of seasonal adjustment packages will improve transparency and comparability of seasonally adjusted time-series across countries.
29.13. Seasonal adjustment and consistency with annual data. Annual trade totals based on seasonal adjustment will not automatically (or conceptually) be equal to the corresponding annual trade totals based on unadjusted data. Specifically, the annual totals of the unadjusted series and the seasonally adjusted series will be equal only when the series are adjusted additively, the seasonal pattern is fixed from one year to the next, and there are no trading-day adjustments. The impact of working days, moving holidays and other calendar effects change from one year to the next. Moving seasonality also implies that the impact of the seasonal effect will vary across years. Nonetheless, the process of ensuring that seasonally adjusted values sum to their unadjusted annual values, known as benchmarking, can be conducted using seasonal adjustment software.
29.14. Direct versus indirect seasonal adjustment. Direct seasonal adjustment is performed if all time series, including aggregates, are seasonally adjusted on an individual basis. Indirect seasonal adjustment is performed if the seasonally adjusted estimate for a time series is derived by combining the estimates for two or more directly adjusted series. Indirect seasonal adjustment should be preferred when the component series that makes up the aggregate series have both distinctively dissimilar seasonal patterns and adjustments of good quality. Direct seasonal adjustment should be the approach of choice when the corresponding series have similar seasonal patterns and summing the series may reduce the amount of unexplained variation.
 Note that optimal direct seasonal adjustment does not preserve additivity; however, it is in general a good practice to give priority to obtaining the best seasonal adjustment of individual series, rather than maintaining additivity. See, e.g., Bank of England, “Prospective change in seasonal adjustment methodology: consultation with users-summary of responses”, Bankstats (Monetary & Financial Statistics) Articles, February 2003. Also available from http://www.bankofengland.co.uk/statistics/ms/articles.htm.