ECOTRIM A program for temporal disaggregation of time series

1. ECOTRIMA program for temporal disaggregation of time series Eurostat – Unit C2 Roberto Barcellan

2. Ecotrim for Windows Ecotrim is a program developed by Eurostat, Directorate C, Economic and Monetary Statistics, Unit C2, Economic accounts . Windows version: based on Visual Basic and C++ Application of advanced temporal disaggregation techniques to economic statistics

3. Forewords • The Ecotrim project has been developed by Eurostat since beginning of 90s • Several versions: GAUSS, Fortran, SAS, Windows • The version 1.01 beta 3 currently available will be the reference for this presentation • Ecotrim for Windows is still a beta version • A first version of the manual will be soon available • For specific technical details related to methodology, please refer to the literature mentioned in the supporting papers • Several users in Europe and outside Europe Application of advanced temporal disaggregation techniques to economic statistics

4. Why Eurostat developed Ecotrim? • ESA 95 paragraph 12.04 • “The statistical methods used for compiling quarterly accounts may differ quite considerably from those used for the annual accounts. They can be classified in two major categories: direct procedure and indirect procedure. • ... On the other hand, indirect procedures are based on temporal disaggregation of the annual accounts data in accordance with mathematical and statistical methods using reference indicators that permit the extrapolation for the current year. • The choice between the different indirect procedures must above all take into account the minimisation of the forecast error for the current year, in order that the provisional annual estimates correspond as closely as possible to the final figures. The choice between these approaches depends, among other things, on the information available at quarterly level”. Application of advanced temporal disaggregation techniques to economic statistics

5. Temporal disaggregationprocess of deriving high frequency data from low frequency data and, if available, related high frequency information ECOTRIM supplies a set of mathematical and statistical techniques to carry out temporal disaggregation Application of advanced temporal disaggregation techniques to economic statistics

6. Temporal disaggregation techniques are a valid support in compiling short-term statistics (e.g. QNA): • Quarterly National Accounts (QNA) give a quarterly breakdown of the figures in the annual accounts • Flash estimates use the available information in the best possible way including, in the framework of a statistical model, the short-term available information and the low frequency data in a coherent way • Monthly indicators of GDP the monthly estimates are derived from the available information respecting the coherence with quarterly data Application of advanced temporal disaggregation techniques to economic statistics

7. Other short-term statistics: • Short-term industrial statistics • Employment • Money and banking statistics in this presentation we focus on QNA Application of advanced temporal disaggregation techniques to economic statistics

8. The present Windows version of the program supplies a range of techniques concerning: • temporal disaggregation of univariate time series by using or not related series and fulfilling temporal aggregation constraints (the methods that ECOTRIM offers, follow the mathematical approach and the optimal, in the least squares sense, approach); • temporal disaggregation of multivariate time series with respect of both temporal and contemporaneous aggregation constraints (in this case too ECOTRIM proposes both adjustment and optimal techniques, in the least squares sense); • forecasting of current year observations by using or not available information on related series. Application of advanced temporal disaggregation techniques to economic statistics

9. Basic ideas - QNA (1) • Temporal disaggregation methods for compiling quarterly accounts are an integral part of the estimation approach. • Their use is more intensive or less intensive according to the main philosophy that characterises the system of quarterly accounts. • The use of mathematical and statistical methods do not necessarily imply a lack of basic information since these models can be used also to improve the quality of the quarterly figures. Application of advanced temporal disaggregation techniques to economic statistics

10. Basic ideas - QNA (2) • Each series is linked to one or more available related quarterly series. • Due to differences in definition and coverage, the account indicators do not give the same value as the series to be estimated (such as in the direct approach) • Their movement can be used to recover the quarterly dynamicsof the unknown aggregate. Application of advanced temporal disaggregation techniques to economic statistics

11. Temporal and Accounting constraint • National accountants are often faced with the estimation of a set of quarterly series linked by some accounting relationship. • Temporal disaggregation methods can also be used in such cases, to give a solution consistent with both temporal and contemporaneous aggregation constraints. Application of advanced temporal disaggregation techniques to economic statistics

12. Characteristics of temporal disaggregation methods (1) • The set of basic information should include statistical variables that are considered as good proxies of the aggregates that have to be estimated • All variables that have a high explanatory power with respect to a specific national accounts aggregate but which do not satisfy (a) have to be eliminated from the set of basic information (for example the interests rate for the estimation of GDP); Application of advanced temporal disaggregation techniques to economic statistics

13. Characteristics of temporal disaggregation methods (2) • The statistical models need not to incorporate any relationships between the aggregates of quarterly accounts that imply economic hypotheses as for example, the relation between consumption and disposable income; • The set of basic information should only include variables associated with the economy of the country for which the quarterly accounts are compiled. This means that the information set is closed; Application of advanced temporal disaggregation techniques to economic statistics

14. Selection of indicators • Choice at high frequency (movements) • Relationships and statistics available only at low frequency (link with the target series) • Experience • Ex-post analysis: statistics (available in Ecotrim), correlation between estimated and related series (levels and growth rates) Application of advanced temporal disaggregation techniques to economic statistics

15. Basic principles • Distribution When annual data are either sums or averages of quarterly data (e.g., GDP, consumption, indexes and in general all flow variables and all average stock variables) • Interpolation When annual value equals by definition that of the fourth (or first) quarter (e.g., population at the end of the year, money stock, and all stock variables) • Extrapolation When estimates of quarterly data are made when the relevant annual data are not yet available Application of advanced temporal disaggregation techniques to economic statistics

16. Estimates have to be consistent and coherent • time consistency quarterly values have to match annual values (for example the sum of quarterly values of the GDP must be equal to the annual value): • accounting coherence quarterly components of an account should respect the accounting constraints (for example, the sum of quarterly values of the GDP expenditure side components should be equal to the corresponding quarterly value of GDP): Application of advanced temporal disaggregation techniques to economic statistics

17. Methods that do not involve the use of related series • Smoothing procedures • Time series methods Basic ideas: • sufficiently smoothed path • coherence with temporal aggregation constraints • these methods can be used when there are serious gaps in basic information (only annual data are available) Application of advanced temporal disaggregation techniques to economic statistics

18. Methods that make use of related series The quarterly path is estimated on the basis of external quarterly information for logically and/or economically related variables. • quarterly information linked to the relevant variable of interest are used • sub-annual or short-term indicators • multivariate applications Application of advanced temporal disaggregation techniques to economic statistics

19. Temporal disaggregation approaches According to the techniques, the accounting constraints and the different amount of basic information used, temporal disaggregation methods can be distinguished in: Univariate Approach Multivariate Approach Smoothing methods Two steps adjustment methods Two steps adjustment methods Regression based methods Time series methods* Regression based methods • static models • dynamic models* * Not in Ecotrim Windows Application of advanced temporal disaggregation techniques to economic statistics

20. Smoothing methods • They typically assume that the unknown quarterly trend can be conveniently described by a function of time such that the necessary condition of satisfying aggregation constraints and the desirable condition of smoothness are both met. • Generally these techniques estimate the quarterly figures by considering a "window" of annual values and a subset of the time series. Starting from these data, the techniques minimise the discrepancy between known annual values and quarterly estimated data. Application of advanced temporal disaggregation techniques to economic statistics

21. Smoothing method within Ecotrim for Windows • Boot , Feibes e Lisman • Minimise the sum of squared first differences between successive disaggregated values (model FD) • Minimise the sum of squared second differences (model SD) • suitable for situation with lack of information • they ensure interpolation estimates for the quarterly breakdown • use of all the information available and give estimation for all the period considered • no extrapolation and diagnostics or confidence bands Application of advanced temporal disaggregation techniques to economic statistics

22. Two steps adjustment methods They divide the process of estimation in two parts: • The first step in indirectly estimating quarterly accounts series is usually the conversion of quarterly indicators into quarterly series which are not consistent with the annual counterpart. We shall refer to this step as preliminary estimation. • At the second step, the preliminary estimates are then processed in order to fit the known annual series, using procedures that we shall refer to as adjustment. In the multivariate case, the second step includes the fulfilment of the contemporaneous accounting constraints Application of advanced temporal disaggregation techniques to economic statistics

23. Procedure of the two steps adjustment methods Preliminary estimation: • direct way, for example sample survey • mathematical-statistical way, for example by using a linear regression relationship between the annual accounts series and the annualised related indicators. But the preliminary quarterly estimates do not generally satisfy the temporal aggregation constraints. • Distribution of the annual discrepancy between the annual aggregate and the aggregated preliminary quarterly estimates • Fitting annual constraints and altering the quarterly path given by the preliminary estimates to the least extent possible. Application of advanced temporal disaggregation techniques to economic statistics

24. Denton • Benchmarking • Movement preservation principle • AFD levels • PFD proportional levels • Weighted matrices Application of advanced temporal disaggregation techniques to economic statistics

25. Time series methods(not in Ecotrim Windows) • Wei and Stram (1990) and Al-Osh(1989) • They are not currently implemented within Ecotrim for Windows but they are present in the Gauss version • The advantage of this procedure is that they provide now-casts » during the year even if no related indicators are available • more sophisticated statistical smoothing methods • they can be used in case of lack of information • ARIMA model based techniques Application of advanced temporal disaggregation techniques to economic statistics

26. Optimal statistical methods • they merge the steps of preliminary estimation and adjustment • one statistically optimal procedure • use of all the available information in the context of a regression model • the model involves annual information and quarterly related information • ensure the annual consistency Application of advanced temporal disaggregation techniques to economic statistics

27. Chow and Lin solution • Chow and Lin (1971) worked out a least-squares optimal solution on the basis that a linear regression model involving the quarterly aggregate series and the related quarterly series will hold • natural and coherent solution to the extrapolation problem. • intensively used in National Statistical Institutes, especially in France, in Italy, Portugal, Belgium and Spain. Application of advanced temporal disaggregation techniques to economic statistics

28. Optimal statistical methods (static models) within Ecotrim for Windows • Different versions of this technique have been developed according to the different hypotheses related to the structure of the error in the regression model. The stochastic error models usually considered when estimating quarterly accounts series are the following: • Model AR(1) Chow and Lin GLS (min SSR of Barbone and others 1981, max Log Bournay and Laroque, 1979); • Random walk model (Fernàndez, 1981); • Random walk-Markov model (Litterman, Min SSR and Max Log). Application of advanced temporal disaggregation techniques to economic statistics

29. Statistics • Rhô • R-squared • Durbin-Watson • Probability of F • T-stat • Reliability indicators (lower value for the range between Min and Max) Application of advanced temporal disaggregation techniques to economic statistics

30. Multivariate models • multivariate dimension • contemporaneous accounting constraints are introduced in the estimation step • temporal and accounting coherence • two approaches: • multivariate benchmarking • BLUE approach Application of advanced temporal disaggregation techniques to economic statistics

31. Regression based methods for the multivariate approach • White noise • Random Walk • No preliminary estimates fulfilling the annual constraint are requested • Here is an extension to the multivariate of the univariate approach • From the statistical point of view is better to use WN or RW but for the practical aspects Rossi and Denton ensure more coherence in terms of growth rates Application of advanced temporal disaggregation techniques to economic statistics

32. Multivariate adjustment A reasonable way to eliminate the discrepancy between a contemporaneously aggregated value and the corresponding sum of disaggregated preliminary quarterly estimates, consists in distributing such a discrepancy according to the weight of each single temporally aggregated series with respect to the contemporaneously aggregated one Application of advanced temporal disaggregation techniques to economic statistics

33. Denton multivariate adjustment Denton’s multivariate adjustment generalises the univariate procedure shown in the univariate case by taking into account some technical devices about (i) the treatment of starting values (Cholette, 1984, 1988) and (ii) the nature of the accounting constraints Preliminary estimates fulfilling the annual constraint are not necessarily requested • Denton AFD • Denton ASD • Denton PFD • Denton PSD Application of advanced temporal disaggregation techniques to economic statistics

34. Rossi multivariate adjustment Preliminary estimates fulfilling the annual constraint are requested Rossi’s procedure can be viewed as a sub-case of Denton’s. The estimated series are forced to satisfy the accounting constraint Application of advanced temporal disaggregation techniques to economic statistics

35. Use of ECOTRIM ECOTRIM is a program that supplies a set of mathematical and statistical techniques to carry out temporal disaggregation. • Structured for Windows 95/98 and Windows NT • Visual Basic and C++ • User friendly It can be used according to two different modes: • interactive mode • batch mode Application of advanced temporal disaggregation techniques to economic statistics

36. Input session Output session • Univariate methods • Boot, Feibes and Lismann • Denton • AR(1) • Fernàndez • Litterman • Multivariate methods • White noise • Random walk • Rossi • Denton Graphs and display Interactive mode Application of advanced temporal disaggregation techniques to economic statistics

37. Batch session • univariate • multivariate Batchcommandfile Output Batch mode ECOTRIM performs temporal disaggregation of several jobs starting from a batch command file. Batch mode is very useful when handling many series. Application of advanced temporal disaggregation techniques to economic statistics

38. Expenditure: households final consumption; government final consumption; gross fixed capital formation; changes in inventories; export; imports. Output: agriculture, hunting, forestry and fish.; industry, including energy; construction; wholesale, retail trade; hotels and rest.; financial, real-estate, renting and business activities; other services activities; FISIM; taxes less subsidies on products. ECOTRIM: A guided ExampleThe compilation of the euro-area and EU quarterly accountsAvailable dataSuppose that you have at your disposal a set of annual data composed by the series of GDP and main expenditure and output components: Application of advanced temporal disaggregation techniques to economic statistics

39. Unique GDP Note that the annual GDP is unique and that the output approach and the expenditure approach are balanced. Annual data cover the period 1991-2002. In addition, Suppose that you have at your disposal a set of quarterly preliminary estimates/indicators to be used for estimating the GDP and the expenditure and output components on a quarterly basis preliminary Quarterly indicators cover the period 1991Q1-2003Q2. Application of advanced temporal disaggregation techniques to economic statistics

40. Objectives The objective of the exercise to obtain quarterly estimates of GDP and expenditure and output components that: • Fulfil the time consistency requirements: the sum of the four quarters of a year is equal to the corresponding annual figure for each variable; • Fulfil the accounting requirements: the sum of the quarterly components is equal to the corresponding quarterly value for GDP both on the expenditure and output side. The available quarterly preliminary estimates/indicators do not satisfy the temporal constraints and the accounting constraint. They give an idea of the quarterly movements of the target variables but do not present the same level as the target variables. Application of advanced temporal disaggregation techniques to economic statistics

41. The approach to the estimate of quarterly figures • The approach to the estimation of the quarterly figures is divided in two steps: • Estimate of each component on the expenditure and output side by respecting the time constraint (the sum of the quarter for the past year has to be equal to the corresponding annual value; • Balancing of the expenditure and output side. Application of advanced temporal disaggregation techniques to economic statistics

42. The univariate methods used Univariate estimates: univariate method of Chow and Lin; • The Chow and Lin method allows to obtain single estimates of each component that respect the annual constraint for the past years (1991-2002) and to obtained the estimates for the quarters in the current year (in the example, 2003Q2). The main idea of the approach is that indicator and target variable satisfy a regression model that is valid both for annual and quarterly data, with the exception of the error structure. From the available annual figures the procedure derives the estimates of the parameters of the regression model. These parameters are then applied to the quarterly model to derive the quarterly figures, including the “extrapolation” for the quarters of the current year. Application of advanced temporal disaggregation techniques to economic statistics

43. The forced multivariate adjustment • Balancing: multivariate Denton procedure. • The Denton multivariate method allows obtaining a balanced set of data that respect the accounting constraints for all the considered period and the annual constraints for the past years. This technique requires an input series that already fulfils the time consistency constraint. Application of advanced temporal disaggregation techniques to economic statistics

44. Annual GDP - euro-zone Application of advanced temporal disaggregation techniques to economic statistics

45. Quarterly indicator Application of advanced temporal disaggregation techniques to economic statistics

46. Annual data and indicator Application of advanced temporal disaggregation techniques to economic statistics

47. Final estimate Application of advanced temporal disaggregation techniques to economic statistics

48. GDP, statistics Application of advanced temporal disaggregation techniques to economic statistics

49. Estimate, full output Application of advanced temporal disaggregation techniques to economic statistics

50. Batch file DI="H:\...\Estimates_expenditure\ecotrim"; DO="H:\...\Estimates_expenditure\ecotrim"; FP="eur12_EXP_CON_KPM95E_qs.PRN"; FR="eur12_EXP_CONDET_KPM95E_qs.PRN"; FL="OUTPUT.LOG"; OW="0"; { MET= 4 ; TA= 1 ; ORDER= 4 ; ("eur12_EXP_AGG_KPM95E_AN.PRN":1); ["eur12_EXP_REL_KPM95E_qs.PRN":1]; PARL=-.99; PARH=+.99; } Application of advanced temporal disaggregation techniques to economic statistics