OECD STESWPOECD STESWPParis 26 June 2007Paris 26 June 2007

DRAFTDRAFTEUROSTAT GUIDELIENS ON EUROSTAT GUIDELIENS ON

SEASONAL ADJUSTMENTSEASONAL ADJUSTMENT

Cristina Calizzani - Gian Luigi MazziCristina Calizzani - Gian Luigi Mazzi

General SchemeGeneral 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 costsSeasonal 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

Cautions:- 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-Treatment1 Pre-Treatment

1.1 Graphical analysis of the series

1.2 National and EU/Euro-area calendars

1.3 Methods for trading/working day adjustment

1.4 Correction for moving holidays

1.5 Outlier detection and correction

1.6 Decomposition model

1.7 Model selection

1.1 Graphical analysis of the series1.1 Graphical analysis of the series

Graphical analysis of the series provides useful information (SA, parameters, problems on data)

Information on:

- length of the series

- presence strange values (zero, outliers..)

- structure of the series (trend, seasonal component, volatility)

- presence of breaks in seasonal behaviour

- decomposition model

More sophisticated graphs (spectrum, autocorrelogram) provide information on the presence of the seasonal component and/or trading-day effect

1.1 Graphical analysis of the series1.1 Graphical analysis of the series

Options: Use of basic graph in the time domain Use of sophisticated graphs (spectrum, autocorrelograms) Use default run of the SA software Graphical analysis of the most important series

Evaluation of alternatives:A.Detailed graphical analysis based on graphs,

autocorrelograms, spectra. The analysis could be complemented with a first explanatory run of the SA software

B.First graphical analysis of the most important series (explanatory first run of the SA software)

C.No graphical analysis is done

1.2 National and EU/Euro-zone 1.2 National and EU/Euro-zone calendarscalendars

Can be used for working/trading-day adjustment

Availability of national calendars under DEMETRA

Tramo-Seats, TSW, X12Arima allow integrating national calendars

through regressors

Construction of EU/Euro-area calendar 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

1.2 National and EU/Euro-zone 1.2 National and EU/Euro-zone calendarscalendars Options:

Use of default calendars Use of national calendars or the Euro-area one as appropriate Definition of series for which calendar adjustment is not

required

Evaluation of alternatives:

A.

B. Use of default calendars (within the tool without reference to national/euro area specificities)

C. No calendar correction despite diagnostic evidence (in this case the ARIMA modelling of the series will be affected) Consequences on decomposition may be important

European aggregates (Direct appraoch) EU/Euro-zone calendars

Indirect geographical adjustment National calendars

1.3 Methods for trading/working day adjustment1.3 Methods for trading/working 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

1.3 Methods for trading/working day adjustment1.3 Methods for trading/working day adjustment

Options No correction 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 RegArima correction (as before but with ARIMA residuals)

Evaluation of alternativesA. RegArima approach (in case of economic rationale for the TDE)

- All pre-test for number of regressors, length and composition of month- Checking for plausibility of effects

B. Regression-based approachC. Purely proportional methods, other adjustments or no adjustment

1.4 Correction for moving holidays1.4 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

When non negligible, such effects should be estimated and removed

Aim: obtaining a seasonally adjusted series whose single-point values are independent of particular calendar effects which occur irregularly across years

1.4 Correction for moving holidays1.4 Correction for moving holidays

Options No correction Correction within proportional adjustment Automatic correction Correction based on an estimation of the duration of the moving

holidays effects

Evaluation of alternativesA. RegArima approach

- pre-test for Easter, other moving holidays effect- Definition of the length of Easter effect on the basis of results of pre-

tests - Checking for plausibility of effects

B. Regression-based approachC. No tests/correction despite diagnostic evidence of such effects

1.5 Outlier detection and correction1.5 Outlier detection and correction

Outliers are abnormal values of the 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 and reintroduced after having estimated calendar/seasonal component

1.5 Outlier detection and correction1.5 Outlier detection and correction

Options Types of outliers to be considered for pre-testing Removal or not of outliers before seasonal adjustment Including or not important outliers in the regression model as

intervention variables

Evaluation of alternativesA. The series should be checked for different outliers

- Remove outliers due to data errors - Adjust out of the series other outliers before seasonal adjustment/re-introduce outliers after estimation calendar/seasonal component- Outliers should be explained using all available information

Outliers with a clear interpretation (severe strikes, changes in government policy ..) are included as regressors in the model

B. As before, but complete automatic procedure according to available tools

C. No preliminary treatment of outliers

1.6 Decomposition model1.6 Decomposition model

How the various components (TC, S, I) combine to form the original series

Default decomposition model is multiplicative in most economic time series

Tramo-Seats only proposes additive/log-additive decomposition X-12-RegARIMA adds a pseudo-additive and a multiplicative decomposition

For series with trends in mean and in variance the log-additive decomposition seems to be the most appropriate one; When only trend in mean is present, the multiplicative decomposition is recommended

For series with zero or negative values, the additive decomposition is automatically selected by SA procedures

The choice of the decomposition model and the differencing orders aim to achieve a stationary series

These 2 decisions impact forecasts, model-based seasonal adjustments and trend-cycle estimates

1.6 Decomposition model1.6 Decomposition model

Options Automatic decomposition model selection Manual decomposition scheme after graphical inspection For series with zero or negative values adding a constant and select

the most appropriate scheme For second order weak-stationary series additive decomposition

Evaluation of alternativesA. Automatic decomposition model selection using appropriate

information criteria after graphical inspection of the series; Special treatment for non positive series (adding a constant and checking the impact on the seasonally adjusted series); Manual selection for more problematic series

A. Fully automatic decomposition model using information criteriaB. Use of a fixed decomposition model (multiplicative for positive

series, additive for non positive series)

1.7 Model selection1.7 Model selection

Model selection: Criteria to select the appropriate model for pre-adjustment,

seasonal adjustment, forecast extension fro SA

Log versus non-log specification of the model

Order of differencing for seasonal and non seasonal part

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

…

Different relevance for model based methods or non parametric ones

1.7 Model selection1.7 Model selection Options

Automatic model selection Model selection based on a set of predefined models Manual model selection

Evaluation of alternativesA. 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 Adjustment2 Seasonal Adjustment

2.1 Choice of SA approach

2.2 Consistency between raw and SA data

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 2.1 Choice of seasonal adjustment approach

Most commonly used seasonal adjustment packages Tramo-Seats

X12ARIMA

Tramo-Seats: model-based approach based on Arima decomposition techniques

X12ARIMA: 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

2.1 Choice of seasonal adjustment approach2.1 Choice of seasonal adjustment approach Options

X12ARIMA Tramo-Seats or TSW X13-AS Structural time series models

Evaluation of alternativesA. Tramo-Seats and X12ARIMA / 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 time series models based on simultaneous representation of the unobserved components of the series within software that can estimate calendar and outliers effects with diagnostics for all components and effects

C. Other production tools

2.2 Consistency between raw and SA data2.2 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 assumption 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 data2.2 Consistency between raw and SA data Options

Do not apply any constraint Apply default constraining techniques (X12ARIMA) Constrain seasonally data to sum up to original data Constrain seasonally adjusted data to sum to trading day ONLY

adjusted data

Evaluation of alternativesA. Do not impose that the sum (average) of raw and SA/calendar

adjusted data should 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. benchmarking methods should be used

C. Impose consistency between seasonally/calendar adjusted data and raw data

2.3 Geographical aggregation: direct versus 2.3 Geographical aggregation: direct versus indirect approachindirect approach

Performing SA at different geographocal aggregation levels: SA either by NSI or Eurostat on national series with same method

and software and European totals derived by aggregating SA national figures (decentralised or centralised indirect approach)

SA directly on European total obtained by aggregation of national not SA/WDA (direct approach)

Each series is SA with different methods and software and the SA European totals derived as aggregation of the SA components (Mixed indirect approach)

National and European figures are independently SA and aggregation constrains imposed ex-post

Neither theoretical nor empirical evidence in favour of one of the approaches

Often strong requirements of consistency between MS data and European figures, especially when additive data (QNA, External Trade, Empl/Unemploiment)

2.3 Geographical aggregation: direct versus 2.3 Geographical aggregation: direct versus indirect approachindirect 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 2.3 Geographical aggregation: direct vs indirect Geographical aggregation: direct vs indirect approachapproach

Evaluation of alternativesA. Direct approach for transparency reasons and in case of lack of

harmonization of national approaches;

Centralized indirect approach is also recommended when subsidiarity principle does apply (external trade, unemployment);

B. Decentralized indirect approach within a common quality assessment framework (where there is a strong user requirement of geographical consistency between national and European aggregates i.e. additivity)

Check for the presence of any residual seasonality in the indirectly adjusted European aggregates

C. Mixed indirect approach

2.4 Sectoral aggregation: direct vs indirect approach2.4 Sectoral aggregation: direct vs indirect approach

Different sectoral aggregation levels Indirect approach: SA sectoral components with same methods

and software and totals derived by aggregating SA sectoral figures

Direct approach: aggregation of raw data and SA of the aggregates

Mixed indirect approach: each sectoral series is SA with different methods and software and the SA totals derived by aggregation of SA components

Aggregated and disaggregated figures are independently SA and aggregation constraints imposed ex-post

For several statistical domains there is often a strong requirement of consistency at various level of classification (QNA, Balance of payments, External trade, Employment)

2.4 Sectoral aggregation: direct vs indirect approach2.4 Sectoral aggregation: direct vs indirect approach

Evaluation of alternatives

A. Both direct or indirect approaches either in case of direct adjustment for the geographical aggregation or no previous 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 to obtain consistency of disaggregated and aggregated estimates (if the adjustments arising from benchmarking have adequate quality)

C. Use of a mixed indirect approach

2.5 Data presentation issues 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 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 2.5 Data presentation issues

Evaluation of alternativesA. Avoid the presentation of trend-cycle data in press releases

- Always raw and SA data

- 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 Policies3 Revisions Policies

3.1 General revision policy

3.2 Timing of revision: Tramo-Seats approach

3.3 Timing of revision: X12Arima approach

3.1 3.1 General revision policy

SA data usually revised revision of raw data

Improved information set

Better estimates of the seasonal pattern

Revision are welcomed because they derive from improved information set

In SA one or more observation can lead to revise several past observations

Trade off between precision in SA data and stability of seasonal adjustment

pattern

Revision should be scheduled in a regular way

No revision should take place between two consecutive releases

3.1 3.1 General revision policy

Options Revise SA data according to the release calendar of the

unadjusted data Revise SA data whenever revisions of raw data occur or at least

once a year Revise SA data more often than scheduled raw data releases

Evaluation of alternativesA) Every time a new data is added, internal check against the best possible seasonally adjusted data. If results computed with forecasted factors differ perceptibly for the best possible adjusted data, then seasonal factors have to be recalculated and SA data revise back in time. Revise only last 3-4 yearsB) Revise SA data once a year or whenever revisions of raw data occur. It is recommended to freeze data as in A);C) Scheduling revision only once a year or even at lower frequency without any a priori evaluation, as well as revising data more often than scheduled raw data releases

3.2 Timing of revision: Tramo-Seats approach3.2 Timing of revision: Tramo-Seats approach

Important to define the timing for the re-identification and re-estimation of Arima models

Normally, the re-estimation of parameters is carried out more frequently than the re-identification re-identification of models

Re-identification takes place usually once per year or even less frequently.

3.2 Timing of revision: Tramo-Seats approach3.2 Timing of revision: Tramo-Seats approach Options

To re-identify and re-estimate models once a year; To re-identify models once a year and re-estimate parameters each

time seasonal adjustment is performed; To specify other timing between re-identification and re-

estimation.

Evaluation of alternativesA) Models are re-identified once per year and parameters are re-estimated every time seasonal adjustment is performed according to the release calendar of raw data (concurrent adjustment). To restrict revisions only to the last three/four years and to freeze previous seasonally adjusted data unless major revisions on raw data occur;B) To re-identify and re-estimate models once a year or whenever unexpected events and/or revisions on raw data occur. It is recommended to freeze data as described in A);C) No re-identification/estimation of models or different timing from those under A) and B), as well as revising data more often than scheduled raw data releases

3.2 Timing of revision: X12Arima approach3.2 Timing of revision: X12Arima approach For the current year seasonally adjusted data can be

computed: by running every month/quarter the seasonal adjustment

procedure (data are revised every month/quarter) by using extrapolated coefficients computed once a year

(data are not revised within the year but only once a year) The first approach increases data accuracy The second one is preferred by users which do not like

continuous revision The use of extrapolated seasonal factors can lead to biased

results when unexpected events occur Revisions should be scheduled in a regular way and possibly

according to the raw data release calendar No revision should take place between two consecutive

releases.

3.2 Timing of revision: X12Arima approach3.2 Timing of revision: X12Arima approach Options

Concurrent adjustment; Concurrent adjustment with only the preceding month and same month of

the previous year revised until December adjustment, when all past adjustment values are updated. This could avoid complaints from some users

Use of extrapolated seasonal factors. Evaluation of alternatives

A) Re-estimate seasonal factors according to the release calendar of raw data (concurrent adjustment). It is recommended to restrict revisions only to the last three/four years and to freeze previous seasonally adjusted data unless major revisions on raw data occur;

B) Concurrent adjustment with updating of only a few past values until December or use of extrapolated seasonal factors with the possibility of modifying them whenever unexpected events and/or revisions in raw data take place. It is recommended to freeze data as in A)

C) Use of purely extrapolated seasonal factors as well as revising seasonal factors more often than scheduled raw data releases

4 Quality of Seasonal Adjustment4 Quality of Seasonal Adjustment

4.1 Validation of seasonal adjustment

4.2 Common quality measures for seasonal adjustment

4.3 Eurostat Quality Report for seasonal adjustment

4.4 Template for seasonal adjustment metadata

4.1 Validation of seasonal adjustment4.1 Validation of seasonal adjustment

• Accurate monitoring needed before acceptance results• Availability of a wide range of quality measures

Absence of residual seasonalityAbsence of residual calendar effectsStability of the seasonal adjusted pattern

Validation by means of:Graphical analysisDescriptive statisticsNon parametric criteriaParametric criteria

4.14.1 Validation of seasonal adjustmentValidation of seasonal adjustment Options

Use an integrate set of graphical, descriptive, non parametric/parametric criteria to check the suitable characteristics of SA data;

Restrict validation to the use of standard measures proposed by different seasonal adjustment tools;

Use only graphical inspection and descriptive statistics to validate the seasonal adjustment

Evaluation of alternativesA) Use an integrate set of graphical, descriptive, non parametric and parametric criteria to validate the seasonal adjustment and run again the SA with a different set of options in case of non acceptance of results. Particular attention to:-absence residual seasonality/calendar effects- absence over-smoothing- absence autocorrelation of the irregular component- stability of the seasonal component

B) Use only default criteria defined within different tools to validate the results and run again the seasonal adjustment as in alternative A) if validation fails;C) No validation of performed seasonal adjustment

4.2 Common quality measures for SA4.2 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

4.2 Common quality measures for SA 4.2 Common quality measures for SA

Options To use specific quality measures for each approach

To use common diagnostics for both approaches

Evaluation of alternativesA. 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

4.3 Eurostat Quality Report for SA4.3 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

4.3 Eurostat Quality Report for SA 4.3 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 alternativesA. 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

4.4 Template for seasonal adjustment metadata 4.4 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

4.4 Template for seasonal adjustment metadata 4.4 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 alternativesA. 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 Adjustment5 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

Do not perform any SA

Stability and reliability problems of Tramo-Seats and X12 when series are long enough to use the tools, 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

Re-specify all parameters involved in pre-treatment and seasonal adjustment more often than in the standard case

Comparative studies on the relative performance of Tramo-Seats and X12 for series shorter than 7-10 years

Inform users about instability problems for series shorter than 7-10 years

5.1 Seasonal adjustment of short time series 5.1 Seasonal adjustment of short time series

Evaluation of alternativesA. 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- Tuning of parameters checked more than once per year

B. SA not performed on too short series

C. Use of non standard tools on short time series

5.2 Treatment of problematic 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 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 alternativesA. SA is performed for problematic series

- Prefer a case by case approach to a standard one- Inform users on the adopted strategy - Consult literature/manual/experts

B. Perform SA only on relevant problematic series and treat other problematic series in a standard way

C. Automatic SA for all series

Thanks for your attention!