Why Seasonally Adjust and How? Approaches X-12-ARIMA, TRAMO/SEATS, X-13 A/S and Tools

1. UNECE Workshop on Short-Term Statistics (STS) and Seasonal Adjustment 14 – 17 March 2011, Astana, Kazakhstan Why Seasonally Adjust and How?Approaches X-12-ARIMA, TRAMO/SEATS, X-13 A/S and Tools Anu PeltolaEconomic Statistics Section, UNECE

2. Overview • What and why • Basic concepts • Methods • Software • Recommendations • Useful references

3. A Coyote Moment Did We Notice the Turning Point?

4. Economic Crises – Statistics • Did we give any warnings? • A responsibility for the statistical offices? A new task? • Important to all users of statistics • Not only to politicians, but also to enterpreneurs and citizens • Statistical offices often have monopoly to analyze detailed data sets • We should not forecast, but draw attention to statistics • Identify changes early, leading indicators, develop more flash estimates -> quality vs. timeliness • Otherwise, a risk of marginalisation of NSOs

5. Economic Crises – Conclusions • Some limits of official statistics were highlighted by the critics: • lack of comparability among countries • need for more timely key indicators • need for statistical indicators in areas of particular importance for the financial and economic crisis Source: Status Report on Information Requirements in EMU

6. Turning Points Trend vs. Year-on-Year RateVolume of Construction

7. Why Seasonally Adjust? • Seasonal effects in raw data conceal the true underlying development • Easier to interpret, reveals long-term development • To aid in comparing economic development • Including comparison of countries or economic activities • To aid economists in short-term forecasting • To allow series to be compared from one month to the next • Faster and easier detection of economic cycles

8. Why Original Data is Not Enough? • Comparison with the same period of last year does not remove moving holidays • If Easter falls in March (usually April) the level of activity can vary greatly for that month • Comparison ignores trading day effects, e.g. different amount of different weekdays • Contains the influence of the irregular component • Delay in identification of turning points

9. Seasonal Adjustment • Seasonal adjustment is an analysis technique that: • Estimates seasonal influences using procedures and filters • Removes systematic and calendar-related influences • Aims to eliminate seasonal and working day effects • No seasonal and working day effects in a perfectly seasonally adjusted series

10. Interpretation of Seasonally Adjusted Data • In a seasonally adjusted world: • Temperature is exactly the same during both summer and winter • There are no holidays • People work every day of the week with the same intensity Source: Bundesbank

11. Filter Based Methods • X-11, X-11-ARIMA, X-12-ARIMA (STL, SABL, SEASABS) • Based on the “ratio to moving average” described in 1931 by Fredrick R. Macaulay (US) • Estimate time series components (trend and seasonal factors) by application of a set of filters (moving averages) to the original series • Filter removes or reduces the strength of business and seasonal cycles and noise from the input data

12. X-11 and X-11-ARIMA X-11 • Developed by the US Census Bureau • Began operation in the US in 1965 • Integrated into software such as SAS and STATISTICA • Uses filters to seasonally adjust data X-11-ARIMA • Developed by Statistics Canada in 1980 • ARIMA modelling reduces revisions in the seasonally adjusted series and the effect of the end-point problem • No user-defined regressors, not robust against outliers

13. X-12-ARIMA http://www.census.gov/srd/www/x12a/ • Developed and maintained by the US Census Bureau • Based on a set of linear filters (moving averages) • User may define prior adjustments • Fits a regARIMA model to the series in order to detect and adjust for outliers and other distorting effects • Diagnostics of the quality and stability of the adjustments • Ability to process many series at once • Pseudo-additive and multiplicative decomposition • X-12-Graph generates graphical diagnostics

14. X-12-ARIMA Source: David Findley and Deutsche Bundesbank

15. Model Based Methods • TRAMO/SEATS, STAMP, ”X-13-ARIMA/SEATS” • Stipulate a model for the data (V. Gómes and A. Maravall) • Models separately the trend, seasonal and irregular components of the time series • Components may be modelled directly or modelling by decomposing other components from the original series • Tailor the filter weights based on the nature of the series

16. TRAMO/SEATS www.bde.es • By Victor Gómez & Agustin Maravall, Bank of Spain • Both for in-depth analysis of a few series or for routine applications to a large number of series • TRAMO preadjusts, SEATS adjusts • Fully model-based method for forecasting • Powerful tool for detailed analyses of series • Only proposes additive/log-additive decomposition TRAMO = Time Series Regression with ARIMA Noise, Missing Observations and Outliers SEATS = Signal Extraction in ARIMA Time Series

17. DEMETRA software http://circa.europa.eu/irc/dsis/eurosam/info/data/demetra.htm • By EUROSTAT with Jens Dossé,Servais Hoffmann, Pierre Kelsen, Christophe Planas, Raoul Depoutot • Includes both X-12-ARIMA and TRAMO/SEATS • Modern time series techniques to large-scale sets of time series • To ease the access of non-specialists • Automated procedure and a detailed analysis of single time series • Recommended by Eurostat

18. X-12-ARIMA vs. TRAMO/SEATS Source: Central Bank of Turkey (2002):Seasonal Adjustment in Economic Time Series.

19. Demetra+ software • Users can choose: • Tramo-Seats model-based adjustments • X-12-ARIMA • One interface • Aims to improve comparability of the two methods • Uses a common set of diagnostics and of presentation tools • Necmettin Alpay Koçak isa member of the testing group

20. Common Guidelines • Use tools and software supported widely • Demetra+ will be supported by Eurostat • Methodological guidelines will be available • Results will be more comparable • Use your national calendars • Dedicate enough human resources to SA • Define a SA strategy • Aim at a clear message to the users • Consider which series serve the purpose of the indicator • Document all relevant choices and events

21. Useful references • Eurostat is preparing a Handbook on Seasonal Adjustment • ESS Guidelines on Seasonal Adjustment http://epp.eurostat.ec.europa.eu/cache/ITY_OFFPUB/KS-RA-09-006/EN/KS-RA-09-006-EN.PDF • Central Bank of the Republic of Turkey (2002). Seasonal Adjustment in Economic Time Series. http://www.tcmb.gov.tr/yeni/evds/yayin/kitaplar/seasonality.doc • Hungarian Central Statistical Office (2007). Seasonal Adjustment Methods and Practices. www.ksh.hu/hosa • US Census Bureau. The X-12-ARIMA Seasonal Adjustment Program.http://www.census.gov/srd/www/x12a/ • Bank of Spain. Statistics and Econometrics Software.http://www.bde.es/servicio/software/econome.htm • Australian Bureau of Statistics (2005). Information Paper, An Introduction Course on Time Series Analysis – Electronic Delivery. 1346.0.55.001. http://www.abs.gov.au/ausstats/abs@.NSF/papersbycatalogue/7A71E7935D23BB17CA2570B1002A31DB?OpenDocument