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Seasonal adjustment


by Eurostat and National Bank of Belgium

In case of any problems or questions, please contact Eurostat Unit B1 Methodology, Quality and Research at:

To download documentation about Demetra+ from CROS portal please click here

Reference page to ESS guidelines on Seasonal adjustment here

For info about the next ESTP course on DEMETRA+ for beginners and advanced users that will be held at Eurostat please consult here


Seasonal adjustment is an important step of the official statistics business architecture and harmonisation of practices has proved to be key element of quality of the output. In this spirit, since the 90s, Eurostat has been playing a role in the promotion, development and maintenance of a software solution (Demetra) freely available for seasonal adjustment in line with established best practices.

In 2008, ESS (European Statistical System) guidelines on SA have been endorsed by the CMFB and the SPC as a framework for seasonal adjustment of PEEIs and other ESS and ESCB economic indicators. ESS guidelines cover all the key steps of the seasonal and calendar adjustment process and represent an important step towards the harmonisation of seasonal and calendar adjustment practices within the ESS and in Eurostat. A common policy for the seasonal and calendar adjustment of all infra-annual statistics will improve the quality and comparability of the national data as well as enhance the overall quality of European to the extent that proper SA tools exist and are available.

The SA Steering Group (the Eurostat-ECB high level group of experts from NSIs and NCBs which has produced the ESS Guidelines for seasonal adjustment) is promoting the development of a flexible software solution for SA to be used within the ESS. The group has drawn its attention on the object oriented technologies used by the R&D Unit of the Department of Statistics of the National Bank of Belgium to develop a series of prototype tools for SA. This has been considered as an adequate framework for the cooperative development of a new generation of sustainable SA tools, enabling the implementation of the ESS guidelines and replacing the previous Demetra whose maintenance and sustainability is put in question.

Demetra+ is a family of modules on seasonal adjustment, which are based on the two leading algorithms in that domain (TRAMO&SEATS@ / X-12-ARIMA). TRAMO&SEATS@ (TRAMO \”Time series Regression with ARIMA noise, Missing values and Outliers\”, and SEATS, \”Signal Extraction in ARIMA Time Series\”, developed by Agustín Maravall and Victor Gómez) and X-12-ARIMA (developed by David Findley and Brian Monsell) are two different methods to seasonally adjust a time series. Both methods can be divided into two main parts: a pre-adjustment step, which removes the \”deterministic\” component of the series by means of a regression model with Arima noises and the decomposition part itself. The two methods use a very similar approach in the first part of the processing but they differ completely in the decomposition part. Their comparison is often difficult, even for the modelling step. More especially, their diagnostics focus on different aspects and their outputs take completely different forms. One of the main features of Demetra+ is to normalize – as much as possible – the different methods. It tries to improve the comparability of the two methods by using as much as possible, a common set of diagnostics and of presentation tools. That fundamental choice implies that a number of routines of both methods have been re-written in Demetra+. That can lead, compared to the original programs, to small discrepancies in diagnostics or in peripheral information that should not alter the general \”message\” provided by the algorithms. Under no circumstances should the main results of the original programs (seasonally adjusted series…) be impacted by that solution.


The technology (Object Oriented components) underlying the toolkit has proved to be a powerful and flexible solution for managing the complexity of seasonal adjustment algorithms and integrating the major well-known SA engines provided by the Bank of Spain and USCB. In addition, it could easily be embedded in many different environments allowing fast developments and extensions.