ECOTRIM A program for temporal disaggregation of time series

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ECOTRIMA program for temporal disaggregation of
time series

• Eurostat Unit C2
• Roberto Barcellan

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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

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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

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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.

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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

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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

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Other short-term statistics

• Short-term industrial statistics
• Employment
• Money and banking statistics
• in this presentation we focus on QNA

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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.

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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.

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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 dynamics of the unknown aggregate.

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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.

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Characteristics of temporal disaggregation
methods (1)

1. The set of basic information should include
   statistical variables that are considered as good
   proxies of the aggregates that have to be
   estimated
2. 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)

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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

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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)

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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

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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)

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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)

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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

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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

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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.

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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

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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

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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.

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Denton

• Benchmarking
• Movement preservation principle
• AFD levels
• PFD proportional levels
• Weighted matrices

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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

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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

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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.

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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).

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Statistics

• Rhô
• R-squared
• Durbin-Watson
• Probability of F
• T-stat
• Reliability indicators (lower value for the range
  between Min and Max)

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Multivariate models

• multivariate dimension
• contemporaneous accounting constraints are
  introduced in the estimation step
• temporal and accounting coherence
• two approaches
• multivariate benchmarking
• BLUE approach

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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

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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

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Denton multivariate adjustment

• Dentons 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

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Rossi multivariate adjustment

• Preliminary estimates fulfilling the annual
  constraint are requested
• Rossis procedure can be viewed as a sub-case of
  Dentons.
• The estimated series are forced to satisfy the
  accounting constraint

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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

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Interactive mode
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Batch mode

• ECOTRIM performs temporal disaggregation of
  several jobs starting from a batch command file.
  
• Batch mode is very useful when handling many
  series.

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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

• 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.

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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.

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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.

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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.

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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.

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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.

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Annual GDP - euro-zone
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Quarterly indicator
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Annual data and indicator
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Final estimate
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GDP, statistics
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Estimate, full output
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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

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Scheme expenditure side
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Discrepancypreliminary vs. constraint
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Preliminary vs. final estimateHousehold
consumption
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GVA construction
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For any information or question about Ecotrim and
to obtain the latest releases related to the
program, please contact

• Mr Roberto BARCELLAN
• EUROPEAN COMMISSION
• Statistical Office
• Directorate C -Unit C2
•  
• Jean Monnet Building
• BECH B3/398
• L-2920 LUXEMBOURG
• Tel. [phone]
• Fax. [phone]
• e-mail roberto.barcellan_at_cec.eu.int