Download
1 / 26
E N D
Whereas chain-linking of annuals in previous years prices is unambiguous, it is not at quarterly frequencies. Contrary to the US, annuals as well as quarters are calculated at average prices of the whole previous year in the EU. For the consecutive construction of quantity indexes, there exist three different methods: • The over-the-year method
The annual-overlap method • The quarterly-overlap method
Three different chain-linking methods blue = over-the-year method green = quarterly-overlap method red = annual-overlap method
Time series properties • Over-the-year method: Breaks in the series (compared to the previous quarter) occur every quarter. Does not represent a time series in a narrower statistical sense. • Annual-overlap method: Breaks in the series (compared to the previous quarter) occur every first quarter of a year. Represents a time series in a narrower statistical sense only within a year. • Quarterly-overlap method: No breaks in the series (compared to the previous quarter) occur. Represents a time series in a narrower statistical sense.
Time consistency (additivity) property • Over-the-year method: approximately time consistent even away from the reference period • Annual-overlap method: fully time consistent • Quarterly-overlap method: not time consistent, especially away from the reference period ⇨ Splitting-up annual discrepancies over quarters by a method generating time series in a narrower sense (proportional Denton procedure, spline functions) does not interfere with the time series properties of the benchmarked series. Note: Quarterly-overlap method + pro-rata distribution of annual discrepancies ≙ annual-overlap method. According to the IMF‘s Quarterly National Accounts Manual (2001, p. 84): ‘Because of the step problem, the pro-rata distribution technique is not acceptable.‘
Differences between the sum of the quarters and annual data in Austrian GDP
Relative differences between the AO- and the Denton benchmarked QO-method
Distribution of annual chain-linking-differences by the AO and the B-QO-method
Consequences for time series modelling of QNA data chain-linked by different methods Why time series modelling of QNA series? • Outlier detection procedures for preparing time series for a following seasonal adjustment are based on time series analysis. • For seasonal adjustment an extrapolation of the series beyond the time series horizon is necessary to apply filter techniques for the recent observations (which are in the focus of interest). All extrapolation methods rely on time series properties. • For TRAMO-SEATS the seasonal component is extracted by factorization of the time series model. For X-12 instead, mathematical filters are applied (making this procedure slightly less dependent on neat time series properties). • For some kind of business cycle analysis (Beveridge-Nelson decomposition, unobserved components models, …)
Models suggested by TRAMO-SEATS Over-the-year method
Quarter-to-quarter percentage changesseasonally and working day adjusted
BC extraction • Seasonally adjusted OTY, AO and B-QO series(by time-series modelling techniques)HP1600-filtered • Unadjusted series (not modelled)BK 32-8 filterd
Co-movement of cyclical components Note: The + (-) sign refers to a lead (lag) vis-à-vis the reference series.
Conclusions • Different quarterly chain-linking methods generate different time series. • Their different time series properties can potentially interfere with modelling outliers, seasonalfactors,BC-components, … • This can lead to different results for analysis based on model pre-processed series. • The turning point detection process itself (not basedon data pre-processed or pre-adjusted by timeseries models) seems to be rather robust to differentquarterly chain-linking methods.
