9 th Euroindicators Working Group Luxembourg, 4 th & 5 th December 2006 Eurostat - Unit D1 Key Indicators for European Policies

EUROSTAT GUIDELINES ON SEASONAL ADJUSTMENT Cristina Calizzani and Gian Luigi Mazzi Doc 185 / 06 Eurostat - Unit D1 Key Indicators for European Policies Item V of the Agenda

General Scheme 0.Seasonal Adjustment: advantages and costs 1.Pre-Treatment 2.Seasonal Adjustment 3.Revision Policies 4.Quality of Seasonal Adjustment 5.Specific issues on Seasonal Adjustment

Seasonal Adjustment: advantages and costs Advantages: -Provide more smoothed and understandable series for analysts -Facilitate comparisons of long/short term movements -Supply users with necessary input for BC analysis, TC decomposition and turning points detection Drawbacks: -SA depends on ‘a priori’ hypothesis -Quality of SA depends on quality of raw data -Lower degree of comparability of data among countries and across statistical domains if clear policies are not defined -SA data are inappropriate for econometric modelling purposes Costs: -Time consuming, significant computer/human resources required -Common and defined IT structure is needed -Inappropriate or low quality SA can give misleading results

1 Pre-Treatment 1.1 National and EU/Euro-zone calendars 1.2 Methods for trading day adjustment 1.3 Correction for moving holidays 1.4 Outlier detection and correction 1.5 Model selection

1.1 National and EU/Euro-zone calendars  Can be used for working/trading-days adjustment  Availability of national calendars under DEMETRA  Construction of EU/Euro-zone calendars by the ECB :  Weighted average of national calendars  Weights derived from the added value of the economic sector for which the specific calendar must be used

1.1 National and EU/Euro-zone calendars  Options:  Use of default calendars  Use of national calendars or the Euro-zone one as appropriate  Definition of series for which calendar adjustment is not required  Evaluation of alternatives: A. B.Use of default calendars C.No correction for working days in presence of calendar effects DirectEU/Euro-zone calendars IndirectNational calendars

1.2 Methods for trading day adjustment  Removal of all effects related to calendar effects  Length of the month  Number of working days per month  Composition of working days in terms of number of Monday, Tuesday, etc…  February length is not constant over years (leap year effect)  Working/trading-days effects as a source of non linearity of time series  Obtaining series with single-point values independent on calendar  Non seasonally adjusted  Seasonally adjusted

1.2 Methods for trading day adjustment  Options  Proportional methods on the bases of the number of days in the month  Regression methods in a multivariate regression framework -With or without correction for the length of the month or leap year -Identification of the most appropriate number of regressors  Evaluation of alternatives A.Regression based methods -All pre-test for number of regressors, length and composition of month -Checking for plausibility of effects B.Default regression-based approach C.Proportional methods

1.3 Correction for moving holidays  Moving holidays occur irregularly in the course of the year  Absence of periodicity  Not removed by standard seasonal filters  Examples of moving holidays: Easter, Pentecost, Ramadan  Moving holidays effect typically defined on a time varying span  Among months  Among quarters  Aim: obtaining a seasonally adjusted series whose single-point values are independent of particular calendar effects which occur irregularly within years

1.3 Correction for moving holidays  Options  No correction  Correction within proportional working day adjustment  Automatic correction  Correction based on an estimation of the duration of the moving holidays effects  Evaluation of alternatives A.Regression based approach -All pre-test for Easter, other moving holidays -Definition of the length of Easter effect on the basis of results of pre- tests -Checking for plausibility of effects B.Default regression-based approach C.No tests/correction

1.4 Outlier detection and correction  Outliers are abnormal values occurring in observed time series  Classification of main outliers  Impulse outliers: abnormal values in isolated points of the series  Transitory changes: series of innovation outliers with transitory effects on the level of the series  Level shifts: series of innovation outliers with constant and permanent effect on the level of the series  Presence of outliers affects model identification and seasonal adjustment  Outliers have to be removed

1.4 Outlier detection and correction  Options  Types of outliers to be considered for pre-testing  Removal or not of outliers before seasonal adjustment  Evaluation of alternatives A.Check according to default options in the tools -Remove outliers due to data errors -Adjust out of the series other outliers before seasonal adjustment -Re-introduce outliers B.As before, but complete automatic procedure according to available tools C.No preliminary treatment of outliers

1.5 Model selection  Model selection:  Criteria to select the appropriate model for pre-adjustment, seasonal adjustment, forecast extension  Log versus non-log specification of the model  Use of additive or multiplicative components  Statistical checking of the adequacy of the estimated model  Analysis of decomposition on the basis of the chosen model  …  Essential step for model-based decomposition  Tramo-Seats

1.5 Model selection  Options  Automatic model selection  Model selection based on a set of predefined models  Manual model selection  Evaluation of alternatives A.Automatic selection within a large number of models: additive/multiplicative, extended order Arima models,... -check for model adequacy using standard statistical tests (normality, heteroskedasticity serial correlation, …) and spectrum diagnostics -use of manual model selection for most important / more problematic series B.As before, but complete automatic procedure C.Selection based on a restricted number of pre-defined models

2 Seasonal Adjustment 2.1 Choice of SA approach: Tramo-Seats versus X12- RegARIMA 2.2 Consistency between raw and SA data and adjustment methods 2.3 Geographical aggregation: direct versus indirect approach 2.4 Sectoral aggregation: direct versus indirect approach 2.5 Data presentation issues

2.1 Choice of seasonal adjustment approach  Most commonly used seasonal adjustment packages  Tramo-Seats  X12-RegARIMA  Tramo-Seats: model-based approach based on Arima decomposition techniques  X12-RegARIMA: non parametric approach based on a set of linear filters (moving averages)  X13-AS: new package containing Tramo-Seats and X12- RegARIMA  Univariate or multivariate structural time series models: STAMP  Regression based methods: Dainties, BV4

2.1 Choice of seasonal adjustment approach  Options  X12-RegARIMA  Tramo-Seats or TSW  X13-AS  Evaluation of alternatives A.Tramo-Seats and X12-RegARIMA / X13-AS -Choice on the basis of past experiences, subjective appreciation, characteristics of the series, etc. -Production tools updated on a regular basis after a sufficiently long testing period B.Structural (univariate or multivariate) time series models based on simultaneous representation of the unobserved components of the series C.Other production tools (Dainties, BV4, etc.)

2.2 Consistency between raw and SA data  Aggregation of SA data coincide with aggregation of NSA data over the year  Cumulative seasonality is zero over the year  No trading day or calendar effects  Unrealistic assumptions, especially in the case of multiplicative models  Strong requirements from many users  Quarterly National Accounts  Balance of Payments  No theoretical justification for this constraint  Consequence: bias on seasonally adjusted data

2.2 Consistency between raw and SA data  Options  Do not apply any constraint  Apply default constraining techniques (X12-RegARIMA)  Constrain seasonally adjusted annual totals to sum to original data annual totals  Constrain seasonally adjusted annual totals to sum to trading day ONLY adjusted original annual totals  Evaluation of alternatives A.The sum (average) of raw and seasonally/working days adjusted data should not necessarily coincide B.Consistency between raw/working days adjusted and seasonally/working days adjusted data can be accepted under particular circumstances, i.e. requirements from users C.Impose consistency between seasonally/working days adjusted data and raw data

2.3 Geographical aggregation: direct versus indirect approach  Performing SA at different aggregation levels :  SA at national level then EU total derived by aggregation of national Seasonally adjusted figures (INDIRECT APPROACH)  SA of the EU total obtained by aggregation of national non Seasonally adjusted or WDA only data (DIRECT APPROACH)  Neither theoretical nor empirical evidence in favour of one of the approaches  Strong requirements from users, especially for additive data (i.e. National Accounts, External Trade, Employment, unemployment)

2.3 Geographical aggregation: direct versus indirect approach  Options  Indirect approach: SA national components series in a centralized/decentralized way with the same software and then derive totals by aggregation of SA components  Mixed indirect approach: SA of national data at NSI level using different approaches and software  Direct approach: aggregation of NSA data and SA of the aggregates  Direct approach with distribution of discrepancies -Use of benchmarking techniques

2.3 Geographical aggregation: direct versus indirect approach  Evaluation of alternatives A.Direct approach for transparency reason and in case of lack of harmonization of national approaches; Centralized indirect approach is also recommended when subsidiarity principle doesn’t apply; B.Decentralized indirect approach within a common quality assessment framework C.Mixed indirect approach (especially when other methods than TS and X12 are used at MS level)

2.4 Sectoral aggregation: direct versus indirect approach Different sectoral aggregation levels  Indirect approach: SA components in a centralized/decentralized way with the same software and then derive totals by aggregation of SA components  Direct approach: aggregation of NSA data and SA of the aggregates  Direct approach with distribution of discrepancies -Use of benchmarking techniques

2.4 Sectoral aggregation: direct versus indirect approach  Evaluation of alternatives A.- Both direct or indirect approaches in case of direct adjustment for the geographical aggregation Choice based on : - characteristics of data (correlation of single components, quality of basic data, etc.) - users' requests (e.g. consistency of components and aggregates ) - Otherwise only indirect adjustment B.Direct approach at any level with benchmarking techniques C.Indirect approach using other methods than TS and X12 should be avoided

2.5 Data presentation issues  SA versus trend-cycle data  Main difference: presence of irregular component  SA data often considered more informative  univariate and multivariate analysis  Trend-cycle data usually preferred for high volatile series and graphical representations  Choice of growth rates to show in press releases  Standard versus annualised  Period on period versus annual

2.5 Data presentation issues  Options  Include only raw data in press releases  Extend the informative content of press releases with one or more of the following transformations: SA series, SA plus WDA series, Trend-cycle series  Present only levels or different kinds of growth rates

2.5 Data presentation issues  Evaluation of alternatives A.Avoid the presentation of trend-cycle data in press releases -raw data, SA and trend-cycle series should be available to users through Eurostat website -Trend-cycle data can be used in press releases for high volatile series (include only graphs) -“period on period” growth rates have to be computed on SA data -annual growth rates have to be computed on NON SA data -avoid annualised growth rates B.Present only seasonally adjusted data C.Presentation of trend-cycle data only; computation of yearly growth rates on SA data

3 Revisions Policies 3.1Timing of revisions and re-estimation of Arima models and coefficients 3.2Concurrent versus extrapolated seasonal factors

3.1 Timing of revisions and re-estimation of Arima models and coefficients  SA data usually revised when new data become available  Changes in the forms and parameters of underlying Arima models  Use of symmetric filters  Re-identification of the Arima models  Arima models slowly changing in time  Re-estimation of the Arima models  Parameters affected by new observations  Re-identification and re-estimation of Arima models relevant mainly for model-based approaches

3.1 Timing of revisions and re-estimation of Arima models and coefficients  Options  Re-identify and re-estimate models once a year  Re-identify models once a year and re-estimate parameters each time seasonal adjustment is performed  Specify other intervals between re-identification and re-estimation  Evaluation of alternatives A.Models are re-identified once per year and parameters are re- estimated every time seasonal adjustment is performed B.To re-identify and re-estimate models once a year C.No re-identification/estimation of models or different timing from those under A) and B)

3.2 Concurrent vs extrapolated seasonal factors  Run the SA procedure every month/quarter: concurrent adjustment  Better accuracy  Data continuously revised  Run the SA procedure once a year and use extrapolated seasonal factors  Revisions concentrated in a single month/quarter of each year  Bias occurring in the presence of unexpected events  Many users dislike revisions  Link between release calendars and timing of revisions  No intermediate revision between two consecutive releases

3.2 Concurrent vs extrapolated seasonal factors  Options  Concurrent adjustment  Concurrent adjustment with only preceding month and same month previous year revised until December adjustment  Use of extrapolated seasonal factors  Evaluation of alternatives A.Concurrent adjustment should be preferred B.Concurrent adjustment with updating few past value until December or use of extrapolated seasonal factors with the possibility of modifying them when unexpected events take place C.Use of purely extrapolated factors

4 Quality of Seasonal Adjustment 4.1 Common quality measures for seasonal adjustment 4.2 Eurostat Quality Report for seasonal adjustment 4.3 Template for seasonal adjustment metadata

4.1 Common quality measures for SA  Specific quality measures developed for Tramo-Seats and X12  Reflecting, at least partially, their different philosophy  Possibility of extending X12 measures to Tramo-Seats and vice versa  Not all quality measures can be generalised  Eurostat contribution to define common quality measures  X13-AS as an ideal framework for a set of common quality measures

4.1 Common quality measures for SA  Options  To use specific quality measures for each approach  To use common diagnostics for both approaches  Evaluation of alternatives A.Use of common measures/diagnostics for the analysis of the quality of seasonal adjustment performed with different tools B.Use of standard quality measures/diagnostics provided by tools C.No use of quality measures/diagnostics to evaluate seasonal adjustment

4.2 Eurostat Quality Report for SA  Development of a Eurostat quality report for SA  In the context of a general quality assessment of infra- annual statistics  Eurostat quality report defined both for massive SA treatment and small scale analysis  Short version  Detailed version  Improvement to the quality report needed in the light of recent developments on SA tools and methods

4.2 Eurostat Quality Report for SA  Options  Use Eurostat quality report  Identify further improvement to Eurostat quality report  Use only the quality measures available in standard tools for seasonal adjustment  Evaluation of alternatives A.Use an improved (to be finalised) version of Eurostat quality report B.Use the existing Eurostat quality report C.No use of any quality framework for the evaluation of seasonal adjustment

4.3 Template for seasonal adjustment metadata  Clarity of SA: appropriate harmonized standard documentation  Special Data Dissemination Standard format (SDDS) of IMF  Development of a SA template for metadata  ECB-Eurostat Task Force on Quarterly National Accounts  Improvement of such template according to recent developments in the field of metadata and SA  SDMX

4.3 Template for seasonal adjustment metadata  Options  Use the existing standard template for SA metadata  Improve the standard template for SA metadata  Include SA information into the general SDDS files  Evaluation of alternatives A.Use of standard (or improved) template for SA metadata B.Include SA information into the general SDDS files C.No methodological information supplied for SA

5 Specific issues on seasonal Adjustment 5 Specific issues on seasonal Adjustment 5.1 Seasonal adjustment of short time series 5.2 Treatment of problematic series

5.1 Seasonal adjustment of short time series 5.1 Seasonal adjustment of short time series  Impossibility of performing standard SA on too short series  Use of non standard software (i.e. Dainties)  Do not perform any SA  Stability and reliability problems of Tramo-Seats and X12 when series are long enough to perform SA, but shorter than 10 years  Several empirical studies analysing the behaviour of Tramo- Seats and X12 on short time series  Adopt a transparent policy to inform users about all problems related to the SA treatment of short time series

5.1 Seasonal adjustment of short time series 5.1 Seasonal adjustment of short time series  Options  No adjustment of series shorter than the minimum requirement for Tramo-Seats and X12  Use of alternative procedures to SA of short time series  Comparative studies on the relative performance of Tramo- Seats and X12 for series shorter than 10 years  Inform users about instability problems for series shorter than 10 years

5.1 Seasonal adjustment of short time series 5.1 Seasonal adjustment of short time series  Evaluation of alternatives A.Use standard tools whenever possible -Extension of the sample and stabilisation of SA using non official back-recalculated time series -Simulations on relative performances of the existing standard tools for short series SA -Inform users on the greater instability of SA data and on used methods -Clear publication policy B.SA not performed on too short series C.Use of non standard tools on short time series

5.2 Treatment of problematic series  Strange features in time series  Impossible to find model with acceptable diagnostics  Absence of a clear signal due to the presence of a dominant irregular component  Unstable seasonality  Large number of outliers  Heteroskedasticity in the series/components  Impossibility of a standard treatment for such series  Ad hoc treatment -Software -Options  Quality of SA problematic series  appropriateness of the adopted strategy

5.2 Treatment of problematic series  Options  Seasonally adjust only recent years of the series  Perform ad hoc SA on all problematic series  Perform ad hoc SA only on relevant problematic series  No ad hoc SA  Evaluation of alternatives A.Restrict SA to the last 7-10 years on problematic series -Prefer a case by case approach -Inform users on the adopted strategy -Not performing SA on certain series B.Perform SA only on relevant problematic series and treat other problematic series in a standard way C.Automatic SA for all series