Seasonal Adjustment in

Official Statistics

Claudia Annoni

Office for National Statistics

Seasonally Adjusted Outputs

• Approximately 50 subject areas across the GSS• Several thousand monthly and quarterly series

Includes:

- Economic (National Accounts, Prices, Business Statistics)

- Socio-economic (Labour Market, Tourism, Transport)

- Demographic (Births, Deaths, Marriages)

Organisation

• Time Series Analysis Branch (MG, ONS)

• Statisticians responsible for datasets across the GSS

• Bank of England

The International Scene

• Other NSIs

• Eurostat - would like to see greater harmonisation

• ECB

• Developers of Methods (e.g. US Bureau, Bank of Spain)

Standard Method for ONS

• Cross-departmental GSS Task Force set up in 1995

• Report and recommendations accepted by GSS(M) in 1996

• X11ARIMA adopted as the standard method

Definition of Seasonal Adjustment

Seasonal adjustment is the process of

removing the variations associated with

the time of year or the arrangement of the

calendar

X11Seasonal Adjustment

Procedure

History• 1954: X=0: first computerised seasonal adjustment program

(X=eXperimental)

• 1965: X-11 (US Bureau of Census)

Main Advantages:

- robust adjustment from extreme value treatment

- several seasonal and trend filters, also for ends of the time series, with filter selection method

- trading day regression

Main Criticisms:

- low quality of the asymmetric filters at the end of the time series

- limited filter choices

- many ad hoc criteria and diagnostics

- possibly too few filters

Procedure Retail Sales in non-specialised stores -predominantly foods

• Original Series (Y = C x S x I )

• Moving average applied to Y gives preliminary estimate of C

• Divide Y by C to leave S x I

• Outliers are identified and replaced in the seasonal and irregular series ( S x I )

• Moving average applied to the modified S x I series gives S

• Dividing Y by S gives a preliminary seasonally adjusted series (SA1)

• Henderson moving average applied to SA1 gives a better trend estimate

REPEAT....................

Orginal Series

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Jan-91 Jan-92 Jan-93 Jan-94 Jan-95 Jan-96 Jan-97 Jan-98 Jan-99

Trend Cycle

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Jul-91 Jul-92 Jul-93 Jul-94 Jul-95 Jul-96 Jul-97 Jul-98

Preliminary estimation of the unmodified SI Ratios

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January SI Graph

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1992 1993 1994 1995 1996 1997 1998 1999

January SI Graph with Replacement values

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1992 1993 1994 1995 1996 1997 1998 1999

January SI Graph with Outliers Replaced

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1992 1993 1994 1995 1996 1997 1998 1999

Seasonal Factors

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Jan-91 Jan-92 Jan-93 Jan-94 Jan-95 Jan-96 Jan-97 Jan-98 Jan-99

Estimation of the Seasonally adjusted Series (SA1)

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Estimation of the Henderson Trend Cycle

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Outlier Indentification and Weighting

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0 0.5 1 1.5 2 2.5 3 3.5 4

Standard Deviations from expected value

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I/S Ratio to select moving averages

X11ARIMA uses the global I/S ratio to select the length of seasonal moving average

I/S < 2.5 3x3 moving average

2.5< I/S < 3.5 recalculate I/S after removing 1year of data

3.5< I/S < 5.5 3x5 moving average

5.5< I/S < 6.5 recalculate I/S after removing 1 year of data

I/S > 6.5 3x9 moving average

I/C Ratio to select moving averages

X11ARIMA uses the global I/C ratio to select the length of trend cycle moving average

I/C < 0.99 9-Term Henderson (5-Term for quarterly)

I/C < 3.49 13-Term Henderson (5-Term for quarterly)

I/C > 3.50 23-Term Henderson (7-Term for Quarterly)

History (…continued)• 1980 X11ARIMA (Statistics CANADA)

Main Advantages:

- higher quality at the end of the time series due to ARIMA extension of the time series

- systemised quality measures (M1 to M11,Q)

- options and diagnostics for indirect and direct seasonal adjustment of aggregated series from component series

Limitations:

- ARIMA modelling not robust against outliers

- Seasonal adjustment not robust against level shifts

ARIMA Modelling

• Models the series assuming that each observation is dependent on past observations

• It allows X11ARIMA to forecast up to three years and backcast one year of data.

• It reduces the size of revisions when new data is added

Automatic ARIMA Modelling

• Models are automatically chosen by the programme using the following order:

(0,1,1) (0,1,1)

(0,1,2) (0,1,1)

(2,1,0) (0,1,1)

(0,2,2) (0,1,1)

(2,1,2) (0,1,1)

Statistics

A model is fitted to the data when:

• Average percentage error in the forecast must be less than 15%

• Chi-Sq. probability must be over 5%

• R-squared value close to 1

• Estimated parameters must not be near 1.00

Consumer Expenditure of BeerJan 1986 - Dec 1997

1700

2200

2700

3200

3700

4200

4700

Jan 86 Jan 87 Jan 88 Jan 89 Jan 90 Jan 91 Jan 92 Jan 93 Jan 94 Jan 95 Jan 96 Jan 97

Short Series

• 3 years for any sort of seasonal adjustment• 5 years to fit an ARIMA model• 5 to automatically select a seasonal moving

average• 5 whole years to constrain to annual totals

Up to 8 - 12 years if possible

Too much data: Out of date information

Too little data : Not enough information

Non- Calendar Data• X11ARIMA is designed to adjust data recorded on a

monthly or quarterly basis• The adjustment may be improved by prior adjusting• Important if statistical months are not the same each

year - moving holidays may include August Bank Holiday and Christmas

• Calenderisation is the process of shifting values from the start or end of the period to the appropriate month - to do this need to know trading day patterns ( i.e. no production on a Sunday)

Aggregate Series

Assume series A, B,C,D are totalled such that aggregate series E = A+B+C+D

To seasonally adjust the aggregate series you have two choices

INDIRECT: SA( aggregate) SA(A)+SA(B)+SA(C)+SA(D)

or

DIRECT

SA(aggregate)=SA(E)

IF ABCD have similar seasonal patterns - DIRECT

IF ABCD have different seasonal patterns - INDIRECT

Note: if you use the direct approach there are additional steps to ensure that the series adds up.

Revisions Policy

• Follow any relevant policy• Revise the seasonal adjustment if the raw data is

revised• Major revisions are the last month/quarter and the

month/quarter of the previous year ago• If constraining to annual totals then must revise all

of any whole year• Revise the seasonal adjustment if revise original

data

X12ARIMA(D Findlay, US bureau of the Census)

• Pre-modelling (REGARIMA)

• More filters

• More diagnostics and graphing facilities

X12ARIMA(D Findlay, US bureau of the Census)

RegARIMA Models(Forecasts, Backcasts,

Preadjustments)

Modeling and ModelComparisonDiagnostics

Enhanced X-11 SeasonalAdjustment

Seasonal AdjustmentDiagnostics

REGARIMA

model ARIMAan is

etc.) components

calendar effects,(outlier regressors fixed ofmatrix a is

vectorparameter a is

modelled, be toseries theisWhen

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TRAMO SEATS(A Maravell, Bank of Spain)

• TRAMO - similar to REGARIMA

• SEATS - decomposes the ARIMA model fitted in TRAMO to perform the decomposition

• Components estimated using Wiener-Kolmogorov filter

STAMP(A Harvey, LSE/Cambridge)

• Structural time series model

• Components estimated using the Kalman filter

• Includes some multivariate time series functions

Advantages of Model Based Methods

• Infinite range of filters

• Assumptions made explicit

• Facilitate inference about time series

• Future extension to multivariate approaches possible

Advantages of Model Based Methods

Provides analytical framework for answering questions such as:

- With what error is seasonality measured?

- How is this error carried through to growth rates?

- How are errors smoothed by averaging over several months?

- Should we use the trend or the seasoanally adjusted series for short-term monitoring?

- Is there significant evidence of a turning point?

Disadvantages of Model Based Methods

• Software underdeveloped

• TRAMO SEATS not user friendly, lacks diagnostics and is poorly supported

• STAMP does not reflect the needs of producers of official statistics (e.g. no calendar adjustments)

• neither method handles seasonal heteroskedasticity

The Future

• National Statistics move to X12ARIMA

• Further development of model based methods

• Synthesis of X12ARIMA and TRAMO SEATS

• Longer-term: development of structural model based approaches, including multivariate seasonal adjustment