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Sources of Revisions of Seasonally Adjusted Real Time Data

This presentation discusses the sources, measurement, and decomposition of revisions in seasonally adjusted real time data. It explores the impact of technical procedures and the revision process on the accuracy of the data. The findings are based on an analysis of various economic indicators in Germany.

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Sources of Revisions of Seasonally Adjusted Real Time Data

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  1. Sources of Revisions ofSeasonally Adjusted Real Time Data Jens Mehrhoff*Deutsche Bundesbank Meeting of the OECD Short-term Economic Statistics Working Party (STESWP)Paris, 23-24 June 2008

  2. Outline of the presentation • Introduction • Measuring revisions • Decomposition approach • Variance decomposition • Summary Sources of Revisions ofSeasonally Adjusted Real Time Data

  3. 1. Introduction • The importance of real time data becomes obvious when one tries to understand economic policy decisions made based on historical data and reconsiders these past situations in the light of more recent data. • Statistical agencies and users of seasonally adjusted real time data alike are interested in it, inter alia in terms of the quality and interpretation of statistics. • Thus, revisions of real time data are a frequently discussed topic. • The contribution is to empirically quantify the uncertainty of seasonally adjusted real time data in terms of revisions and decompose them into two sources. Sources of Revisions ofSeasonally Adjusted Real Time Data

  4. 1. Introduction • Let ut be a seasonally time series, where ct,st and it represent a trend-cycle, seasonal and irregular component, respectively: • (1) ut = ctstit • The aim of seasonal adjustment is to calculate the seasonally adjusted time series at: • (2) at = ut / st • Its relative period-to-period changes in per cent are denoted t: • (3) t = (at / at–1) – 1 Sources of Revisions ofSeasonally Adjusted Real Time Data

  5. 2. Measuring revisions • Per cent revisions of the seasonally adjusted time series at are defined as the relative deviation of the most recent estimate at|T from the first one at|t: • (4) rta = (at|T / at|t) – 1 • Revisions of per cent period-to-period changes Dt are measured in percentage points: • (5) rt = t|T – t|t Sources of Revisions ofSeasonally Adjusted Real Time Data

  6. 2. Measuring revisions • Equation (2) for the seasonally adjusted time series (at = ut / st) illustrates that, generally, revisions to seasonally adjusted real time data have two separate but inter-related sources. • One source is the technical procedure of the method used for seasonal adjustment (responsible for st). • The other is the revision process of unadjusted data in real time (ut). Sources of Revisions ofSeasonally Adjusted Real Time Data

  7. 2. Measuring revisions Figure 1: Sources of revisions Sources of Revisions ofSeasonally Adjusted Real Time Data

  8. 2. Measuring revisions • A simple approach to the decomposing of revisions is: • (6) rta = rts + rtu • However, in general the above equality does not hold in practice: • (7) Var(rts + rtu) = Var(rts) + 2  Cov(rts, rtu) + Var(rtu) Cov(rts, rtu) ≠ 0 • It follows that: “The whole is greater than the sum of its parts.” Aristotle Sources of Revisions ofSeasonally Adjusted Real Time Data

  9. 2. Measuring revisions Sources of Revisions ofSeasonally Adjusted Real Time Data

  10. 3. Decomposition approach • Data used in this study are: • Unadjusted real time data (rebased to the current base year) • X-12-ARIMA procedure (latest available, ie holding user settings incl. RegARIMA model parameters constant) • Seasonally readjusted real time data (using 1. and 2.) Sources of Revisions ofSeasonally Adjusted Real Time Data

  11. 3. Decomposition approach • Period covered is from the beginning of 1991 to the end of 2006. • Analysis of revisions is based on the six-year period from 1996 to 2001. • Seasonal adjustment is rerun with the latest data and information available. • For seasonal adjustment official specification files are used. Sources of Revisions ofSeasonally Adjusted Real Time Data

  12. 3. Decomposition approach • Fixed effects heterogeneous panel regression model: • (8) • Slope coefficients are allowed to vary across time series to capture their unique properties. • Estimated slope coefficients i could be used to calculate curve elasticities I, employing average absolute revisions Ri: • (9) Sources of Revisions ofSeasonally Adjusted Real Time Data

  13. 4. Variance decomposition • Investigated time series are important business cycle indicators for Germany: • Real gross domestic product (quarterly, flow, index) • Employment (monthly, stock, persons) • Output in the manufacturing sector (monthly, flow, index) • Orders received by the manufacturing sector (monthly, flow, index) • Retail trade turnover (monthly, flow, index) Sources of Revisions ofSeasonally Adjusted Real Time Data

  14. 4. Variance decomposition Figure 2: Average absolute revisions Sources of Revisions ofSeasonally Adjusted Real Time Data

  15. 4. Variance decomposition Sources of Revisions ofSeasonally Adjusted Real Time Data

  16. 4. Variance decomposition Sources of Revisions ofSeasonally Adjusted Real Time Data

  17. 4. Variance decomposition • 260 observations were included. Coefficients of determination are high for both models at R² = 0.99. Statistical tests indicate model adequacy. • Results for levels clearly indicate the importance of unadjusted real time data revisions and those for period-to-period changes do not contradict them. • However, it is worth taking a closer look at the latter. At the end of the time series a two or three-period moving average (MA) is often used in practice. This lowers standard errors as noise is partially smoothed out. Sources of Revisions ofSeasonally Adjusted Real Time Data

  18. 4. Variance decomposition Sources of Revisions ofSeasonally Adjusted Real Time Data

  19. 4. Variance decomposition • For short-term business cycle analysis, predicting the correct sign of period-to-period changes is crucial. By calculating moving averages, the likelihood of estimating the wrong sign decreases. • Thus, revisions of unadjusted real time data become more important as their elasticity increases absolutely and relatively, and the revisions themselves do not have such a big influence as the sign does not change extraordinarily often. Sources of Revisions ofSeasonally Adjusted Real Time Data

  20. 5. Summary • It can be concluded that revisions of unadjusted real time data play an important role when explaining revisions of seasonally adjusted real time data for Germany as their elasticities were greater than those of seasonal adjustment. • Furthermore, this analysis confirmed a well-known result for the recent past: the current domain of uncertainty of seasonal adjustment depends heavily on the time series analysed and their properties. Sources of Revisions ofSeasonally Adjusted Real Time Data

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