A model based approach for benchmarking seasonally adjusted time - - PowerPoint PPT Presentation

10-12 May 2006

A model based approach for benchmarking seasonally adjusted time series

Susanne Buijtenhek

Conference on Seasonality, Seasonal Adjustment and their implications for Short-Term Analysis and Forecasting

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A model based approach for benchmarking seasonally adjusted time series

Susanne Buijtenhek Statistics Netherlands

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Introduction

– Seasonal adjustment – Inconsistencies may arise

– Quarters do not add up to annual totals – Aggregates not equal to sum of parts

– Restoring consistency

– Indirect method: simple, but ‘noisy’ results – Direct method: to be continued…

Temporal Contemporaneous

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Problem

Can we create consistent seasonally adjusted time series without disturbing growth rates?

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Benchmarking model

– Quadratic minimization under restrictions – Minimization

– Minimizing adaptations made on quarterly growth rates (Denton, 1971) – Taking into account the reliability of time series (Stone et al., 1942)

– Restrictions

– Providing temporal and contemporaneous consistency

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Experiment

Seasonally adjusted quarterly time series for GDP (Y) Consumption (C) Gross fixed capital formation (I) Export (E) Import (M) Increase in stocks (IS) Y = C + I + IS + E - M Census X12 ARIMA

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GDP: absolute levels

GDP: directly and indirectly seasonally adjusted

104000 106000 108000 110000 112000 114000 116000 1 2 3 4 1 2 3 4 1 2 3 4 2001 2002 2003 Quarter Value (Mln euros) Direct method Indirect method

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GDP: growth rates

GDP: directly and indirectly seasonally adjusted

• 1,5
• 1,0
• 0,5

0,0 0,5 1,0 1,5 2,0 2,5 3,0 1 2 3 4 1 2 3 4 1 2 3 4 2001 2002 2003 Quarter Value (%) Direct method Indirect method

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Results for benchmarking model

– Three scenarios differing in reliability weights – Only current prices – Results for quarterly growth rates –Tested for 1977-2004 time series measured by coefficient of variation

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First scenario: all variables equally reliable

Qua rte rly grow th ra te of e x port

• 4,0
• 3,0
• 2,0
• 1,0

0,0 1,0 2,0 3,0 1 2 3 4 1 2 3 4 1 2 3 4 2001 2002 2003 Quar te r Value (%) Res ult Original

Incre a se in stocks

• 1500
• 1000
• 500

500 1000 1 2 3 4 1 2 3 4 1 2 3 4 2001 2002 2003 Qu ar te r Value (million Euro) Res ult Original Qu ar te r ly gr o w th r ate o f GDP

• 0,5

0,0 0,5 1,0 1,5 2,0 2,5 3,0 1 2 3 4 1 2 3 4 1 2 3 4 2001 2002 2003 Quar te r Value (%) Res ult Original Quar te r ly gr o w th r ate o f p r ivate co ns um p tion

• 1,0
• 0,5

0,0 0,5 1,0 1,5 2,0 2,5 1 2 3 4 1 2 3 4 1 2 3 4 2001 2002 2003 Qu ar te r Value (%) Res ult Original

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Second scenario: GDP more reliable

Quar te rly grow th rate of GDP

• 0,5

0,0 0,5 1,0 1,5 2,0 2,5 3,0 1 2 3 4 1 2 3 4 1 2 3 4 2001 2002 2003 Quarte r Value (%) Result Original

Incre a se in stocks

• 1500
• 1000
• 500

500 1000 1 2 3 4 1 2 3 4 1 2 3 4 2001 2002 2003 Quar te r Value (million Euro) Result Original Quarte r ly grow th rate of private cons um ption

• 1,0
• 0,5

0,0 0,5 1,0 1,5 2,0 2,5 1 2 3 4 1 2 3 4 1 2 3 4 2001 2002 2003 Quar te r Value (%) Result Original

Qua rte rly grow th ra te of e x port

• 4,0
• 3,0
• 2,0
• 1,0

0,0 1,0 2,0 3,0 1 2 3 4 1 2 3 4 1 2 3 4 2001 2002 2003 Quarte r Value (%) Result Original

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Third scenario: Increase in stocks less reliable

Quarterly growth rate of GDP

• 0,5

0,0 0,5 1,0 1,5 2,0 2,5 3,0 1 2 3 4 1 2 3 4 1 2 3 4 2001 2002 2003 Quarter Value (%) Result Original

Increase in stocks

• 1500
• 1000
• 500

500 1000 1500 1 2 3 4 1 2 3 4 1 2 3 4 2001 2002 2003 Quarter Value (million Euro) Result Original Quarterly growth rate of private consumption

• 1,0
• 0,5

0,0 0,5 1,0 1,5 2,0 2,5 1 2 3 4 1 2 3 4 1 2 3 4 2001 2002 2003 Quarter Value (%) Result Original

Quarterly growth rate of export

• 4,0
• 3,0
• 2,0
• 1,0

0,0 1,0 2,0 3,0 1 2 3 4 1 2 3 4 1 2 3 4 2001 2002 2003 Quarter Value (%) Result Original Quarterly growth rate of GDP

• 0,5

0,0 0,5 1,0 1,5 2,0 2,5 3,0 1 2 3 4 1 2 3 4 1 2 3 4 2001 2002 2003 Quarter Value (%) Result Original

Increase in stocks

• 1500
• 1000
• 500

500 1000 1500 1 2 3 4 1 2 3 4 1 2 3 4 2001 2002 2003 Quarter Value (million Euro) Result Original Quarterly growth rate of private consumption

• 1,0
• 0,5

0,0 0,5 1,0 1,5 2,0 2,5 1 2 3 4 1 2 3 4 1 2 3 4 2001 2002 2003 Quarter Value (%) Result Original

Quarterly growth rate of export

• 4,0
• 3,0
• 2,0
• 1,0

0,0 1,0 2,0 3,0 1 2 3 4 1 2 3 4 1 2 3 4 2001 2002 2003 Quarter Value (%) Result Original Quarte rly grow th rate of GDP

• 0,5

0,0 0,5 1,0 1,5 2,0 2,5 3,0 1 2 3 4 1 2 3 4 1 2 3 4 2001 2002 2003 Quarte r Value (%) Result Original

Incre a se in stocks

• 1500
• 1000
• 500

500 1000 1500 1 2 3 4 1 2 3 4 1 2 3 4 2001 2002 2003 Quarte r Value (million Euro) Result Original Quarte rly grow th rate of private cons um ption

• 1,0
• 0,5

0,0 0,5 1,0 1,5 2,0 2,5 1 2 3 4 1 2 3 4 1 2 3 4 2001 2002 2003 Quarte r Value (%) Result Original

Qua rte rly grow th ra te of e x port

• 4,0
• 3,0
• 2,0
• 1,0

0,0 1,0 2,0 3,0 1 2 3 4 1 2 3 4 1 2 3 4 2001 2002 2003 Quarte r Value (%) Result Original

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Conclusion

When initial differences are large, quarterly growth rates of variables may be disturbed significantly! and… Reliability weights are not related to the origin

• f the statistical discrepancies: no basis on

which to choose between scenarios