ECOTRIM A program for temporal disaggregation of time series Eurostat – Unit C2 Roberto Barcellan.
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ECOTRIM
A program for temporal
disaggregation of time series
Eurostat – Unit C2
Roberto Barcellan
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++
27 November 2003
OECD, Paris
Application of advanced temporal disaggregation
techniques to economic statistics
2
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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Application of advanced temporal disaggregation
techniques to economic statistics
3
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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techniques to economic statistics
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Temporal disaggregation
process 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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techniques to economic statistics
5
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 shortterm 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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Application of advanced temporal disaggregation
techniques to economic statistics
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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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techniques to economic statistics
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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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techniques to economic statistics
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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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techniques to economic statistics
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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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techniques to economic statistics
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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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techniques to economic statistics
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Characteristics of temporal disaggregation
methods (1)
a)
The set of basic information should include statistical variables
that are considered as good proxies of the aggregates that
have to be estimated
b)
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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techniques to economic statistics
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Characteristics of temporal disaggregation
methods (2)
c)
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;
d)
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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techniques to economic statistics
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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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techniques to economic statistics
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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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techniques to economic statistics
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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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Application of advanced temporal disaggregation
techniques to economic statistics
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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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techniques to economic statistics
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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
Smoothing methods
Two steps adjustment methods
Time series methods*
Regression based methods
static models
dynamic models*
Multivariate Approach
Two steps adjustment methods
Regression based methods
* Not in Ecotrim Windows
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techniques to economic statistics
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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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techniques to economic statistics
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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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techniques to economic statistics
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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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techniques to economic statistics
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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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Application of advanced temporal disaggregation
techniques to economic statistics
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Denton
Benchmarking
Movement preservation principle
AFD
levels
PFD
proportional levels
Weighted matrices
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techniques to economic statistics
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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 nowcasts » 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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Application of advanced temporal disaggregation
techniques to economic statistics
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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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Application of advanced temporal disaggregation
techniques to economic statistics
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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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techniques to economic statistics
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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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Application of advanced temporal disaggregation
techniques to economic statistics
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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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Application of advanced temporal disaggregation
techniques to economic statistics
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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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Application of advanced temporal disaggregation
techniques to economic statistics
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Regression based methods
multivariate approach
for
the
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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Application of advanced temporal disaggregation
techniques to economic statistics
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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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Application of advanced temporal disaggregation
techniques to economic statistics
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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
Denton
Denton
Denton
AFD
ASD
PFD
PSD
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techniques to economic statistics
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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
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Application of advanced temporal disaggregation
techniques to economic statistics
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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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OECD, Paris
Application of advanced temporal disaggregation
techniques to economic statistics
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Interactive mode
Input session
Univariate methods
Multivariate methods
•
Boot, Feibes and Lismann
•
White noise
•
Denton
•
Random walk
•
AR(1)
•
Rossi
•
Fernàndez
•
Denton
•
Litterman
Output session
Graphs and
display
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techniques to economic statistics
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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.
Batch
command
file
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OECD, Paris
Batch session
• univariate
Output
• multivariate
Application of advanced temporal disaggregation
techniques to economic statistics
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ECOTRIM: A guided Example
The compilation of the euro-area and EU
quarterly accounts
Available data
Suppose 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.
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OECD, Paris
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.
Application of advanced temporal disaggregation
techniques to economic statistics
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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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Application of advanced temporal disaggregation
techniques to economic statistics
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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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Application of advanced temporal disaggregation
techniques to economic statistics
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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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techniques to economic statistics
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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 (19912002) 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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techniques to economic statistics
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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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techniques to economic statistics
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Annual GDP - euro-zone
E u ro -a re a , G D P , c o n s ta n t p ric e s 1 9 9 5
6 400 000.0
6 200 000.0
6 000 000.0
5 800 000.0
5 600 000.0
5 400 000.0
5 200 000.0
5 000 000.0
9
19
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OECD, Paris
1
9
19
2
9
19
3
9
19
4
9
19
5
9
19
6
9
19
7
9
19
8
9
19
9
0
20
Application of advanced temporal disaggregation
techniques to economic statistics
0
0
20
1
0
20
2
44
Quarterly indicator
E u r o -z o n e , q u a r te r ly in d ic a to r
1 600 000
1 550 000
1 500 000
1 450 000
1 400 000
1 350 000
1 300 000
1 250 000
1 200 000
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Annual data and indicator
A n n u a l v s . in d ic a to r
1 6 0 0 0 0 0 .0
1 5 5 0 0 0 0 .0
1 5 0 0 0 0 0 .0
1 4 5 0 0 0 0 .0
1 4 0 0 0 0 0 .0
1 3 5 0 0 0 0 .0
1 3 0 0 0 0 0 .0
1 2 5 0 0 0 0 .0
1 2 0 0 0 0 0 .0
1
4
7
10 13 16 19 22 25 28 31 34 37 40 43 46 49
B 1 G M IN D
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B 1GM A NN
Application of advanced temporal disaggregation
techniques to economic statistics
46
Final estimate
An n u a l v s . fin a l
1 6 0 0 0 0 0 .0
1 5 5 0 0 0 0 .0
1 5 0 0 0 0 0 .0
1 4 5 0 0 0 0 .0
1 4 0 0 0 0 0 .0
1 3 5 0 0 0 0 .0
1 3 0 0 0 0 0 .0
1 2 5 0 0 0 0 .0
1 2 0 0 0 0 0 .0
1
4
7
10 13 16 19 22 25 28 31 34 37 40 43 46 49
B 1GM A NN
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OECD, Paris
B 1 G M F IN
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47
GDP, statistics
T h e va lu e o f th e p a ra m e te r is:
D e p e n d e n t va ria b le s
0 .7 0 2 3 4 6
1
--------------------------------------------------------------------------------------------------------------------------------------------------------------V a ria b le
E stim a te S td E rro r t-S ta t
--------------------------------------------------------------------------------------------------------------------------------------------------------------CONSTANT
-4 0 8 4 5 .3
6 9 0 9 .0 5
-5 .9 1
B1G M _KPM 95E_Q S
1 .0 4
0
2 1 0 .5 2
--------------------------------------------------------------------------------------------------------------------------------------------------------------V a lid C a se s
12
D e g re e s o f fre e d o m
10
T o ta l S S
1 .0 8 E + 1 1
R e sid u a l S S
24402792
R -S q u a re d
1
R b a r-S q u a re d
1
S T D e rro r o f e st
1 5 6 2 .1 4
L o g -lik e h o o d
1 1 0 .7 9
F (2 ,1 0 )
4 4 3 2 0 .5 6
P ro b a b ility o f F
0 .2 5
A k a ik e In fo C rite rio n
1 4 .8 6
H e te ro sk . C o n d itio n n u m b e r
ND
D u rb in -W a tso n
1 .8 7
Ja rq u e -B e ra n o rm a lity sta t.
0 .3 2
B o x-P ie rce sta tistic
0 .0 8
B o x-P ie rce sta tistic
0 .8 9
L ju n g B o x Q -sta tistic
0 .1
L ju n g B o x Q -sta tistic
1 .2 3
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Estimate, full output
E -B 1 G M F lo w A R (1 )M IN S S R
________________________________________________________________________________
D a te
V a l.
S td .
R e lia b .
Low
H ig h
D e v.
In d .
199101 1275993
9 7 5 .9 2
0 .0 8 1 2 7 3 8 1 8 1 2 7 8 1 6 7
199102 1279190
7 2 5 .2 9
0 .0 6 1 2 7 7 5 7 4 1 2 8 0 8 0 6
199103 1278653
7 4 7 .3 9
0 .0 6 1 2 7 6 9 8 8 1 2 8 0 3 1 8
199104 1290833
9 2 0 .8 6
0 .0 7 1 2 8 8 7 8 1 1 2 9 2 8 8 5
199201 1310309
9 0 2 .1 2
0 .0 7 1 3 0 8 2 9 9 1 3 1 2 3 1 9
199202 1300632
7 2 5 .3
0 .0 6 1 2 9 9 0 1 6 1 3 0 2 2 4 8
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…
…
…
…
…
…
199403
200102
200103
200104
200201
200202
200203
200204
200301
200302
1324011
1557465
1560110
1558513
1563885
1571309
1574866
1575812
1576201
1574970
7 2 5 .2 6
7 2 6 .4 2
7 2 5 .2 4
9 0 0 .1 4
9 2 2 .7
7 4 8 .9 2
7 2 5 .3 9
9 7 9 .7 9
1 3 6 0 .9 6
1 5 4 2 .5 3
0 .0 5
0 .0 5
0 .0 5
0 .0 6
0 .0 6
0 .0 5
0 .0 5
0 .0 6
0 .0 9
0 .1
1322396
1555846
1558494
1556507
1561829
1569640
1573250
1573629
1573169
1571533
1325627
1559083
1561726
1560518
1565941
1572978
1576482
1577995
1579233
1578407
Application of advanced temporal disaggregation
techniques to economic statistics
49
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
G D P (q1) =
P C (q1) +
G C (q1) +
G F C F (q1) +
C I(q1) +
E X P (q1) -
IM P (q1)
G D P (q2) =
P C (q2) +
G C (q2) +
G F C F (q2) +
C I(q2) +
E X P (q2) -
IM P (q2)
G D P (q3) =
P C (q3) +
G C (q3) +
G F C F (q3) +
C I(q3) +
E X P (q3) -
IM P (q3)
G D P (q4) =
P C (q4) +
G C (q4) +
G F C F (q4) +
C I(q4) +
E X P (q4) -
IM P (q4)
G D P (a)
P C (a) +
G C (a)
G F C F (a)
C I(a)
E X P (a)
IM P (a)
=
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+
+
+
Application of advanced temporal disaggregation
techniques to economic statistics
-
51
Discrepancy
preliminary vs. constraint
D is c re p a n c ie s p re lim in a ry v s . c o n s tra in t
2 5 0 0 .0
2 0 0 0 .0
1 5 0 0 .0
1 0 0 0 .0
5 0 0 .0
0 .0
-5 0 0 .0
-1 0 0 0 .0
-1 5 0 0 .0
1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002
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Preliminary vs. final estimate
Household consumption
P re lim in a ry v s . fin a l h o u s e h o ld c o n s u m p tio n
9 5 0 0 0 0 .0
9 0 0 0 0 0 .0
8 5 0 0 0 0 .0
8 0 0 0 0 0 .0
7 5 0 0 0 0 .0
7 0 0 0 0 0 .0
1
4
7
10 13 16 19 22 25 28 31 34 37 40 43 46 49
S e rie s1
27 November 2003
OECD, Paris
S e rie s2
Application of advanced temporal disaggregation
techniques to economic statistics
53
GVA construction
P re lim in a ry v s . fin a l
79000
78500
78000
77500
77000
76500
76000
75500
75000
74500
74000
1999
2000
2001
P RE L
27 November 2003
OECD, Paris
2002
RE S
Application of advanced temporal disaggregation
techniques to economic statistics
54
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. (+352) 4301 35802
Fax. (+352) 4301 33879
e-mail: [email protected]
27 November 2003
OECD, Paris
Application of advanced temporal disaggregation
techniques to economic statistics
55