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

Conference on Seasonality, Seasonal Adjustment and their implications for Short-Term Analysis and Forecasting 10-12 May 2006 A model based approach for benchmarking seasonally adjusted time series Susanne Buijtenhek

A model based approach for benchmarking seasonally adjusted time series Susanne Buijtenhek Statistics Netherlands 1

Introduction – Seasonal adjustment Temporal – Inconsistencies may arise – Quarters do not add up to annual totals – Aggregates not equal to sum of parts Contemporaneous – Restoring consistency – Indirect method: simple, but ‘noisy’ results – Direct method: to be continued… 2

Problem Can we create consistent seasonally adjusted time series without disturbing growth rates? 3

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 4

Experiment Census X12 ARIMA 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 5

GDP: absolute levels GDP: directly and indirectly seasonally adjusted 116000 114000 Value (Mln euros) 112000 110000 108000 106000 104000 1 2 3 4 1 2 3 4 1 2 3 4 2001 2002 2003 Quarter Direct method Indirect method 6

GDP: growth rates GDP: directly and indirectly seasonally adjusted 3,0 2,5 2,0 Value (%) 1,5 1,0 0,5 0,0 -0,5 -1,0 -1,5 1 2 3 4 1 2 3 4 1 2 3 4 2001 2002 2003 Quarter Direct method Indirect method 7

Results for benchmarking model – Three scenarios differing in reliability weights measured by – Only current prices coefficient of variation – Results for quarterly growth rates –Tested for 1977-2004 time series 8

First scenario : all variables equally reliable Qu ar te r ly gr o w th r ate o f GDP Quar te r ly gr o w th r ate o f p r ivate co ns um p tion 3,0 2,5 2,5 2,0 1,5 2,0 Value (%) Value (%) 1,0 1,5 1,0 0,5 0,0 0,5 -0,5 0,0 -1,0 -0,5 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 2001 2002 2003 2001 2002 2003 Qu ar te r Quar te r Res ult Original Res ult Original Qua rte rly grow th ra te of e x port Incre a se in stocks 3,0 1000 Value (million Euro) 2,0 500 1,0 Value (%) 0 0,0 -1,0 -500 -2,0 -1000 -3,0 -4,0 -1500 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 2001 2002 2003 2001 2002 2003 Quar te r Qu ar te r Res ult Original Res ult Original 9

Second scenario : GDP more reliable Quar te rly grow th rate of GDP Quarte r ly grow th rate of private cons um ption 3,0 2,5 2,5 2,0 2,0 1,5 Value (%) Value (%) 1,5 1,0 1,0 0,5 0,5 0,0 0,0 -0,5 -0,5 -1,0 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 2001 2002 2003 2001 2002 2003 Quarte r Quar te r Result Original Result Original Qua rte rly grow th ra te of e x port Incre a se in stocks 1000 3,0 Value (million Euro) 2,0 500 1,0 Value (%) 0 0,0 -1,0 -500 -2,0 -1000 -3,0 -4,0 -1500 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 2001 2002 2003 2001 2002 2003 Quarte r Quar te r Result Original Result Original 10

Third scenario : Increase in stocks less reliable Quarterly growth rate of GDP Quarte rly grow th rate of GDP Quarterly growth rate of GDP Quarte rly grow th rate of private cons um ption Quarterly growth rate of private consumption Quarterly growth rate of private consumption 3,0 3,0 3,0 2,5 2,5 2,5 2,5 2,5 2,5 2,0 2,0 2,0 Value (%) Value (%) 2,0 2,0 2,0 1,5 1,5 1,5 Value (%) Value (%) Value (%) Value (%) 1,5 1,5 1,5 1,0 1,0 1,0 1,0 1,0 1,0 0,5 0,5 0,5 0,5 0,5 0,5 0,0 0,0 0,0 0,0 -0,5 0,0 0,0 -0,5 -0,5 -0,5 -1,0 -0,5 -0,5 -1,0 -1,0 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 1 2 2 3 3 4 4 1 1 2 2 3 3 4 4 1 1 2 2 3 3 4 4 1 1 2 2 3 3 4 4 1 1 2 2 3 3 4 4 1 1 2 2 3 3 4 4 2001 2001 2001 2002 2002 2002 2003 2003 2003 2001 2001 2001 2002 2002 2002 2003 2003 2003 Quarte r Quarter Quarter Quarte r Quarter Quarter Result Result Result Original Original Original Result Result Result Original Original Original Incre a se in stocks Quarterly growth rate of export Qua rte rly grow th ra te of e x port Quarterly growth rate of export Increase in stocks Increase in stocks Value (million Euro) 1500 1500 1500 3,0 3,0 3,0 Value (million Euro) Value (million Euro) 2,0 2,0 2,0 1000 1000 1000 Value (%) 1,0 1,0 1,0 Value (%) Value (%) 500 500 500 0,0 0,0 0,0 0 0 0 -1,0 -1,0 -1,0 -500 -500 -500 -2,0 -2,0 -2,0 -1000 -1000 -1000 -3,0 -3,0 -3,0 -4,0 -1500 -1500 -1500 -4,0 -4,0 1 2 3 4 1 2 3 4 1 2 3 4 1 1 1 2 2 2 3 3 3 4 4 4 1 1 1 2 2 2 3 3 3 4 4 4 1 1 1 2 2 2 3 3 3 4 4 4 1 1 2 2 3 3 4 4 1 1 2 2 3 3 4 4 1 1 2 2 3 3 4 4 2001 2002 2003 2001 2001 2001 2002 2002 2002 2003 2003 2003 2001 2001 2002 2002 2003 2003 Quarte r Quarte r Quarter Quarter Quarter Quarter Result Original Result Original Result Result Original Original Result Result Original Original 11

Conclusion When initial differences are large, quarterly growth rates of variables may be disturbed significantly! and… Reliability weights are not related to the origin of the statistical discrepancies: no basis on which to choose between scenarios 12