1
Revisions in Seasonal Adjustment Methods:
an Empirical Comparison of
X-12-ARIMA & SEATS
Jens Dossé*
Christophe Planas*
*Consultants to Eurostat, Bâtiment Jean Monnet C5/98,
L – 2920 Luxembourg
Revised Version, September 1996
1 Introduction
Most of seasonal adjustment procedures involve moving average filters.
The difference between moving average filters mainly lies in the way
that the filters are constructed. With methods like X-12-ARIMA (using
the X-11 decomposition), the filter is empirical in the sense that it does
not depend on the statistical properties of the series under analysis. On
the other hand, the ARIMA-model-based signal extraction method as
implemented in the program SEATS uses the information obtained from
the modelling of the series to estimate the components.
In both cases, the filters used are symmetric, involving past and
future realisations of the observed series. For large enough samples, the
application of the filters around the central periods yields the so-called
final estimators. For the most recent periods, no symmetric filter can be
applied, and a preliminary estimator has to be considered instead. An
optimal preliminary estimator can be obtained by replacing the
unknown’s future observations by their forecasts (see Cleveland and
Tiao 1976). The forecast errors imply that the preliminary estimates will
be contaminated by an error, termed revision error. As new observations
become available, forecasts are updated and eventually replaced by the
observed values, and the preliminary estimate is revised. Since the
seasonal adjusted series and the trend estimate for the concurrent period
2
is of most interest to short-term macroeconomic policy makers, the size
of the revisions is then a critical point in a decomposition procedure.
This note discusses and compares the revisions obtained with the
use of an empirical filter as in X-12-ARIMA and with an ARIMA-
model-based approach as in SEATS on the basis of an empirical
investigation.
2 Revision in preliminary estimates
Suppose that one wish to decompose a series into a seasonal
t
s plus
non-seasonal component
t
n according to:
t
t
t
n
s
x
+
=
(2.1)
where additivity may be obtained after a log-transformation. The non-
seasonal component
t
n can be further decomposed into a trend
t
p plus
an irregular component
t
u . Let
( )B
sν
denote the filter used to compute
the final estimator of the seasonal component:
( )
t
s
t
x
B
s
ν
=
ˆ
(2.2)
The filter
( )B
sν
is symmetric and can be written as
( )
+
=L
B
sν
L
+
+
+
−
F
B
1
0
1
ν
ν
ν
. In the case of the model-based approach (cf.
SEATS),
( )B
sν
corresponds to the Wiener-Kolmogorov filter, while in
the case of X-12-ARIMA,
( )B
sν
may correspond to one of the so-called
3 by 3, 3 by 5 or 3 by 9 seasonal MA filter.
Suppose that the correlation structure of the series
t
x is well
described by the model:
( )
t
t
t
t
a
B
a
a
x
ψ
ψ
=
+
+
=
− L
1
1
(2.3)
where
t
a is a Gaussian variable and ( )B
ψ
is a polynomial which can be
3
infinite. Inserting (2.3) into (2.2), then the final estimator of
t
s is given
as:
( ) ( )
( )
t
s
t
s
t
a
B
a
B
B
s
ξ
ψ
ν
=
=
ˆ
(2.4)
where
( )
( ) ( )
L
L
+
+
+
+
=
=
−
F
B
B
B
B
s
s
s
s
s
1
0
1
ξ
ξ
ξ
ψ
ν
ξ
. A preliminary
estimate
k
t
t
s
+
/
ˆ
of
t
s obtained at time
k
t +
is simply obtained by taking
the expectation of the final estimator
t
ŝ conditional on the information
available at time
k
t +
:
( )
[
]
[
]
[
]
( )
t
k
s
t
k
sk
s
s
s
t
k
sk
k
sk
s
s
s
k
t
t
s
k
t
k
t
t
a
B
a
F
F
B
a
F
F
F
B
E
a
B
E
s
ξ
ξ
ξ
ξ
ξ
ξ
ξ
ξ
ξ
ξ
ξ
=
=
+
+
+
+
+
=
=
+
+
+
+
+
+
+
+
=
=
=
−
+
+
−
+
+
+
L
L
L
L
L
1
0
1
1
1
1
0
1
/
ˆ
(2.5)
where use has been made of the fact that the innovations can not be
forecasted. The filter
( )B
k
sξ
corresponds to the filter
( )B
sξ
truncated in
k
F
. The revision
k
R in the preliminary estimate of
t
s obtained at time
k
t +
is then simply obtained as:
∑
∞
+
=
+
+ =
−
=
1
/
ˆ
ˆ
k
i
i
t
si
k
t
t
t
k
a
s
s
R
ξ
(2.6)
The revisions follow thus a moving average process, and standard
results (see Pierce 1980) show that the revisions are convergent. The
update in the preliminary after one further observation is given by:
1
,

,
0

,
ˆ
ˆ
1
1
/
1
/
−
=
=
−
=
+
+
+
+
+
+
T
k
a
s
s
r
k
t
sk
k
t
t
k
t
t
k
K
ξ
.
(2.7)
4
It is clear that different forecasts and different filters imply different
revision patterns.
The result (2.5) also allows us to point out the following sources of
revisions when new observations are added:
• The update of the forecasts.
• The re-estimation of the parameters of the observed series model
yields an updated polynomial ( )B
ψ
, and thus a new polynomial
( )B
ξ
will be obtained (see (2.4)). Notice that in a model-based
approach, an updated filter
( )B
sν
would also be obtained.
• The new observations may affect the identification of the model
for the observed series, giving another form of the polynomial
( )B
ψ
.
• Since the model for the observed series and the optimal filter are
related, it can be expected that a discrepancy between the
properties of the model for forecasting and those of the filter in
use may induce large revision. For example, if unstable seasonal
patterns are predicted while the filter in use is well suited for a
stable seasonality, then some large revisions may be produced.

These considerations have led us to set up an experimental design that
we present now.


3 Experimental Design

Twenty-four monthly time series have been analysed. These series are
French import and export series (nomenclature Nec02, codes 01-12)
starting in January 1980 and ending in December 1994, that is along a
sample of 180 observations. Prior outlier removing and correction
5
for special effects such that trading days and Easter effect have been
performed before the series were sent to X-12-ARIMA and to SEATS.
For every series, the last three years have been removed and a
shorter sample is first considered. That is, a number
36
=
T
of
observations are initially suppressed. The analysis concentrates on the
revisions in the preliminary estimates in the last period in the short
sample. The preliminary estimates considered are the seasonally
adjusted series and the trend estimates. Every time a new observation is
added, new estimates are computed and the revisions in the previous
estimates are straightforwardly available. In particular, the value of k
r is
obtained for every estimate. The estimators obtained after the adding of
the 36th observation is taken as final, yielding
k
R .
Three different ways of dealing with the forecasting model and its
parameters are undertaken: first, the model and its parameter is fixed;
second, the model is fixed but the parameters re-estimated; three, the
model is re-identified/selected and re-estimated every time a new
observation is added.
The parameters sent to SEATS and X-12-ARIMA are given in the
appendix. The two programs have been made running as much as
possible in an automatic way. The statistics used to analyse the results
are:

• Absolute Revision Variation (ARV):


%
100
ˆ
36
/
2
0
1
⋅
−
=
+
−
=
+
∑
t
t
T
k
k
k
s
r
r
ARV
(3.8)

• Smoothness of Revisions (SMR):


(
)
%
100
ˆ
2
2
36
/
2
0
2
1
⋅
−
=
+
−
=
+
∑
t
t
T
k
k
k
s
r
r
SMR
(3.9)
6
• Sum of Squared Revisions (SQR):


%
100
ˆ
2
2
36
/
1
0
2
⋅
=
+
−
=
∑
t
t
T
k
k
s
r
SQR
(3.10)

• Mean Convergence (MC):
Write:


1
,

,
0

%,
100
0
2
−
=
⋅
= ∑ =
T
k
SQR
r
C
k
i
i
k
K
(3.11)

Then,


∑
−
=
=
1
0
1 T
k
k
C
T
MC
(3.12)

• Smoothness of Convergence (SC):
(
)
∑
−
=
+ −
=
2
0
2
1
T
k
k
k
C
C
SC
(3.13)
The first three measures have been standardised so as to yield results
interpretable in proportion of the level of the final estimators. This
standardisation was introduced because the use of different approaches
may lead to different final estimators. Although the differences have
been found often negligible, the correction facilitates the interpretation
of the results.
7
4 Revision
in Seasonal Adjusted Series: Results
of the Comparison
(i) For the 24 series, the re-estimation of the models does not
significantly modify the results: when the models are taken as fixed,
whether the parameter are set or re-estimated does not much affect the
results. On the contrary, proceeding to a re-identification/selection of
the model before re-estimating the parameters have a significant impact.
The SQR statistics indicates that larger revisions are obtained.
(ii) When the model is fixed and for the majority of the cases seen,
the model-based approach (SEATS) yields smaller revisions than with
an empirical filter approach (X-12-ARIMA). This can be seen on the
SQR tables.
(iii) As read from the ARV and SMR figures, X-12-ARIMA often
implies erratic revisions while the model-based approach yields much
smoother revision. This holds whether the model is set or not.
(iv) The convergence may be faster with X-12-ARIMA than with
SEATS (see the MC plot). However, this effect was often related to
relatively large revisions when the first new observations were added.
The plot of the smoothness of the convergence, which shows an as
smooth convergence of the SEATS preliminary estimates as this of the
X-12-ARIMA ones, confirms this.
5 Revision in Trends: Some Theoretical Consid-
erations
The comparison of the revisions in the trend preliminary estimates has
come out to be more difficult for the reason that X-12-ARIMA
estimates trends with a Henderson 13-term moving average filter, and
then suggests the users to select another filter if needed. Furthermore,
depending on the series under analysis, the Henderson 13-term moving
average filter may be more concentrated around the low frequencies
8
than the model-based trend. In that case, the SEATS trend corresponds
to a shorter-term trend and the X-12-ARIMA trend shows longer terms
movements. The comparison of the revisions is thus biased, the two
programs estimating much different trends.
Some points out about the size of the revisions in the trend
preliminary estimators may however be worked. In particular, a result
derived in Maravall and Planas (1995) shows that when a time series
displays a stable (alternatively unstable) pattern, then the component
catching this feature must be made as stable (unstable) as possible to
minimise the variance of the estimation error. In the case of the trend
component, if a time series shows a stable long-run path, then the trend
estimator must be made as stable as possible to be more accurate. In the
model-based approach, the filter for estimating the trend is derived from
the model for the observed series. An empirical filter is instead selected
not strictly in relation with the properties of the series under analysis,
and thus may take benefit from more freedom in its design. In
particular, it may perfectly be that the empirical filter would be more
concentrated around the low frequencies that the filter obtained in the
model-based approach. In that case, lower revisions may be expected.
To check if investigate that point, we have focused the attention on
the time series displaying the most stable long-term pattern, namely
the series Frexp04. The empirical filter for estimating a long-term
trend as been taken as the standard 23-term Henderson filter. The
revision in the estimates of the trend from SEATS, 13-term and 23-term
Henderson filter (X-12-ARIMA) obtained in the last period when up to
3 years of observations are added are presented in appendix. The most
striking figure is that the model-based filter always yields lower
revisions. That can be seen simply from the spectra of the filters
designed to estimate the trend: the SEATS one appears to be much
more concentrated at the low frequency, yielding a more stable
estimator and, as a consequence, less revisions. This illustrates a result
in Maravall and Planas: the narrowest filter more accurately estimates a
stable trend.
France export, part 1
10
100
1000
10000
100000
8001
8101
8201
8301
8401
8501
8601
8701
8801
8901
9001
9101
9201
9301
9401
Date
Logarithmic scaleFrExp01/3
FrExp03/3
FrExp05
FrExp06
FrExp10
FrExp12
9
France export, part 2
10
100
1000
10000
100000
8001
8101
8201
8301
8401
8501
8601
8701
8801
8901
9001
9101
9201
9301
9401
Date
Logarithmic scaleFrExp02
FrExp04
FrExp07
FrExp08
FrExp09
FrExp11
10
France import, part 1
100
1000
10000
100000
8001
8101
8201
8301
8401
8501
8601
8701
8801
8901
9001
9101
9201
9301
9401
Date
Logarithmic scaleFrImp01
FrImp02
FrImp03
FrImp07
FrImp08
FrImp11
11
France import, part 2
100
1000
10000
100000
8001
8101
8201
8301
8401
8501
8601
8701
8801
8901
9001
9101
9201
9301
9401
Date
Logarithmic scaleFrImp04
FrImp05
FrImp06
FrImp09
FrImp10
FrImp12
12
SA revisions of Seats with re-identified models (all time series)
-600
-400
-200
0
200
400
600
r0
r1
r2
r3
r4
r5
r6
r7
r8
r9 r10 r11 r12 r13 r14 r15 r16 r17 r18 r19 r20 r21 r22 r23 r24 r25 r26 r27 r28 r29 r30 r31 r32 r33 r34 r35
Revisions rk (updates in preliminary) during the last three years
13
SA revisions of X-12-Arima with re-selected models (all time series)
-600
-400
-200
0
200
400
600
r0
r1
r2
r3
r4
r5
r6
r7
r8
r9 r10 r11 r12 r13 r14 r15 r16 r17 r18 r19 r20 r21 r22 r23 r24 r25 r26 r27 r28 r29 r30 r31 r32 r33 r34 r35
Revisions rk (updates in preliminary) during the last three years
14
Trend revisions of Seats with re-identified models (all time series)
-600
-400
-200
0
200
400
600
r0
r1
r2
r3
r4
r5
r6
r7
r8
r9 r10 r11 r12 r13 r14 r15 r16 r17 r18 r19 r20 r21 r22 r23 r24 r25 r26 r27 r28 r29 r30 r31 r32 r33 r34 r35
Revisions rk (updates in preliminary) during the last three years
15
Trend revisions of X-12-Arima with re-selected models (all time series)
-600
-400
-200
0
200
400
600
r0
r1
r2
r3
r4
r5
r6
r7
r8
r9 r10 r11 r12 r13 r14 r15 r16 r17 r18 r19 r20 r21 r22 r23 r24 r25 r26 r27 r28 r29 r30 r31 r32 r33 r34 r35
Revisions rk (updates in preliminary) during the last three years
16
SA revisions of Seats with re-estimated model parameters (all time series)
-600
-400
-200
0
200
400
600
r0
r1
r2
r3
r4
r5
r6
r7
r8
r9 r10 r11 r12 r13 r14 r15 r16 r17 r18 r19 r20 r21 r22 r23 r24 r25 r26 r27 r28 r29 r30 r31 r32 r33 r34 r35
Revisions rk (updates in preliminary) during the last three years
17
SA revisions of X-12-Arima with re-estimated model parameters (all time series)
-600
-400
-200
0
200
400
600
r0
r1
r2
r3
r4
r5
r6
r7
r8
r9 r10 r11 r12 r13 r14 r15 r16 r17 r18 r19 r20 r21 r22 r23 r24 r25 r26 r27 r28 r29 r30 r31 r32 r33 r34 r35
Revisions rk (updates in preliminary) during the last three years
18
Trend revisions of Seats with re-estimated model parameters (all time series)
-600
-400
-200
0
200
400
600
r0
r1
r2
r3
r4
r5
r6
r7
r8
r9 r10 r11 r12 r13 r14 r15 r16 r17 r18 r19 r20 r21 r22 r23 r24 r25 r26 r27 r28 r29 r30 r31 r32 r33 r34 r35
Revisions rk (updates in preliminary) during the last three years
19
Trend revisions of X-12-Arima with re-estimated model parameters (all time series)
-600
-400
-200
0
200
400
600
r0
r1
r2
r3
r4
r5
r6
r7
r8
r9 r10 r11 r12 r13 r14 r15 r16 r17 r18 r19 r20 r21 r22 r23 r24 r25 r26 r27 r28 r29 r30 r31 r32 r33 r34 r35
Revisions rk (updates in preliminary) during the last three years
20
SA revisions of Seats with fixed model parameters (all time series)
-600
-400
-200
0
200
400
600
r0
r1
r2
r3
r4
r5
r6
r7
r8
r9 r10 r11 r12 r13 r14 r15 r16 r17 r18 r19 r20 r21 r22 r23 r24 r25 r26 r27 r28 r29 r30 r31 r32 r33 r34 r35
Revisions rk (updates in preliminary) during the last three years
21
SA revisions of X-12-Arima with fixed model parameters (all time series)
-600
-400
-200
0
200
400
600
r0
r1
r2
r3
r4
r5
r6
r7
r8
r9 r10 r11 r12 r13 r14 r15 r16 r17 r18 r19 r20 r21 r22 r23 r24 r25 r26 r27 r28 r29 r30 r31 r32 r33 r34 r35
Revisions rk (updates in preliminary) during the last three years
22
Trend revisions of Seats with fixed model parameters (all time series)
-600
-400
-200
0
200
400
600
r0
r1
r2
r3
r4
r5
r6
r7
r8
r9 r10 r11 r12 r13 r14 r15 r16 r17 r18 r19 r20 r21 r22 r23 r24 r25 r26 r27 r28 r29 r30 r31 r32 r33 r34 r35
Revisions rk (updates in preliminary) during the last three years
23
Trend revisions of X-12-Arima with fixed model parameters (all time series)
-600
-400
-200
0
200
400
600
r0
r1
r2
r3
r4
r5
r6
r7
r8
r9 r10 r11 r12 r13 r14 r15 r16 r17 r18 r19 r20 r21 r22 r23 r24 r25 r26 r27 r28 r29 r30 r31 r32 r33 r34 r35
Revisions rk (updates in preliminary) during the last three years
24
Absolute Revision Variation for all seasonally adjusted and trend series
0
5
10
15
20
25
30
35
0
5
10
15
20
25
30
35
Seats
X-12-ArimaSA Model free
Trend Model free
SA Model order fixed
Trend Model order fixed
SA Model param. fixed
Trend Model param. fixed
N° of series for which ARV(Seats) < ARV(X-11): 131/142
25
Smoothness of Revisions for all seasonally adjusted and trend series
0
10
20
30
40
50
60
70
0
10
20
30
40
50
60
70
Seats
X-12-ArimaSA Model free
Trend Model free
SA Model order fixed
Trend Model order fixed
SA Model param. fixed
Trend Model param. fixed
N° of series for which SMR(Seats) < SMR(X-11): 127/142
26
Sum of Squared Revisions for all seasonally adjusted and trend series
0
10
20
30
40
50
60
0
10
20
30
40
50
60
Seats
X-12-ArimaSA Model free
Trend Model free
SA Model order fixed
Trend Model order fixed
SA Model param. fixed
Trend Model param. fixed
N° of series for which SQR(Seats) < SQR(X-11): 126/142
27
Mean Convergence for all seasonally adjusted and trend series
0500000100000015000002000000250000030000000
500000
1000000
1500000
2000000
2500000
3000000
Seats
X-12-ArimaSA Model free
Trend Model free
SA Model order fixed
Trend Model order fixed
SA Model param. fixed
Trend Model param. fixed
N° of series for which MC(Seats) < MC(X-11): 62/142
28
Smoothness of Convergence for all seasonally adjusted and trend series
100100001000000100000000100000000001E+121E+14100
10000
1000000
100000000
10000000000
1E+12
1E+14
Seats
X-12-ArimaSA Model free
Trend Model free
SA Model order fixed
Trend Model order fixed
SA Model param. fixed
Trend Model param. fixed
N° of series for which SC(Seats) < SC(X-11): 70/142
29
40
60
80
100
120
140
160
180
200
0
20
40
60
80
100
120
140
160
180
EXP04: Original Series
Trend revisions with fixed model parameters for series FrExp04
-1
-0.5
0
0.5
1
1.5
2
2.5
r0
r1
r2
r3
r4
r5
r6
r7
r8
r9 r10 r11 r12 r13 r14 r15 r16 r17 r18 r19 r20 r21 r22 r23 r24 r25 r26 r27 r28 r29 r30 r31 r32 r33 r34 r35
Revisions rk (updates in preliminary) during the last three years
FrExp04 Seats trend
FrExp04 X-12-Arima trend (Henderson-13)
FrExp04 X-12-Arima trend (Henderson-23)
31
32
Parameters sent to Seats and X-12-Arima:
Model parameters fixed:
FrExp01
Seats input:
D=1,BD=1,P=0,BP=0,Q=1,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=2,
TH(1)=-0.458662,
BTH(1)=-0.646929,
TRAMO=-1,BLQT=15.573744,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(2 1 2)(0 1 1)
ar=(-0.6146149903E+00f
0.2810814997E+00f)
ma=(-0.1942233453E+00f
0.6335310999E+00f
0.6486130414E+00f)}
x11{mode=mult trendma=13 seasonalma=s3x5 save=(d11 d12)}
check{save=(acf)}
FrExp02
Seats input:
D=1,BD=1,P=0,BP=0,Q=1,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=2,
TH(1)=-0.368447,
BTH(1)=-0.601682,
TRAMO=-1,BLQT=18.250837,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(0 1 2)(0 1 1)
ma=( 0.3132496774E+00f
0.1165852982E+00f
0.6061667409E+00f)}
x11{mode=mult trendma=13 seasonalma=s3x5 save=(d11 d12)}
check{save=(acf)}
FrExp03
Seats input:
D=1,BD=0,P=0,BP=1,Q=1,BQ=0,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=2,
BPHI(1)=-0.201888,
TH(1)=-0.706600,
TRAMO=-1,BLQT=21.535236,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(0 1 1) (0 1 1)
ma=( 0.7203044275E+00f
0.7243152389E+00f)}
x11{mode=mult trendma=23 seasonalma=s3x5 save=(d11 d12)}
check{save=(acf)}
33
FrExp04
Seats input:
D=1,BD=1,P=0,BP=0,Q=1,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=2,
TH(1)=-0.774064,
BTH(1)=-0.923241,
TRAMO=-1,BLQT=27.665483,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(2 1 0)(0 1 1)
ar=(-0.7038447493E+00f
-0.4339817706E+00f)
ma=( 0.8899731440E+00f)}
x11{mode=mult trendma=23 seasonalma=s3x5 save=(d11 d12)}
check{save=(acf)}
FrExp05
Seats input:
D=1,BD=1,P=0,BP=0,Q=1,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=2,
TH(1)=-0.589691,
BTH(1)=-0.652684,
TRAMO=-1,BLQT=15.123951,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(2 1 2)(0 1 1)
ar=( 0.2011812314E+00f
-0.2173513383E+00f)
ma=( 0.9082461034E+00f
-0.4553338938E+00f
0.6273839741E+00f)}
x11{mode=mult trendma=13 seasonalma=s3x5 save=(d11 d12)}
check{save=(acf)}
FrExp06
Seats input:
D=1,BD=1,P=2,BP=0,Q=0,BQ=0,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=2,
PHI(1)=0.560617,
PHI(2)=0.304828,
TRAMO=-1,BLQT=26.825666,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(0 1 2)(0 1 1)
ma=( 0.6531437910E+00f
-0.2369674316E+00f
0.2524437642E+00f)}
x11{mode=mult trendma=13 seasonalma=s3x5 save=(d11 d12)}
check{save=(acf)}
FrExp07
Seats input:
D=1,BD=1,P=0,BP=0,Q=1,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=2,
TH(1)=-0.706218,
34
BTH(1)=-0.648650,
TRAMO=-1,BLQT=8.929244,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(0 1 1)(0 1 1)
ma=( 0.7073814950E+00f
0.6534618659E+00f)}
x11{mode=mult trendma=23 seasonalma=s3x5 save=(d11 d12)}
check{save=(acf)}
FrExp08
Seats input:
D=1,BD=1,P=0,BP=0,Q=2,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=2,
TH(1)=-0.933254,
TH(2)=0.372568,
BTH(1)=-0.381034,
TRAMO=-1,BLQT=11.891964,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(0 1 1)(0 1 1)
ma=( 0.7630920875E+00f
0.4253977234E+00f)}
x11{mode=mult trendma=13 seasonalma=s3x5 save=(d11 d12)}
check{save=(acf)}
FrExp09
Seats input:
D=1,BD=1,P=0,BP=0,Q=1,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=2,
TH(1)=-0.743045,
BTH(1)=-0.593829,
TRAMO=-1,BLQT=18.527110,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(0 1 1)(0 1 1)
ma=( 0.7449801036E+00f
0.5928487864E+00f)}
x11{mode=mult trendma=23 seasonalma=s3x5 save=(d11 d12)}
check{save=(acf)}
FrExp10
Seats input:
D=1,BD=1,P=0,BP=0,Q=1,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=2,
TH(1)=-0.696577,
BTH(1)=-0.534302,
TRAMO=-1,BLQT=7.808433,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(0 1 2)(0 1 1)
ma=( 0.6885028428E+00f
35
0.1484695287E-01f
0.5331679452E+00f)}
x11{mode=mult trendma=13 seasonalma=s3x5 save=(d11 d12)}
check{save=(acf)}
FrExp11
Seats input:
D=1,BD=1,P=0,BP=0,Q=1,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=2,
TH(1)=-0.543608,
BTH(1)=-0.762261,
TRAMO=-1,BLQT=11.599968,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(0 1 1)(0 1 1)
ma=( 0.5438274305E+00f
0.7756838981E+00f)}
x11{mode=mult trendma=13 seasonalma=s3x5 save=(d11 d12)}
check{save=(acf)}
FrExp12
Seats input:
D=1,BD=1,P=1,BP=0,Q=0,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=2,
PHI(1)=0.477178,
BTH(1)=-0.899710,
TRAMO=-1,BLQT=35.070401,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(0 1 1) (0 1 1)
ma=( 0.4141482226E+00f
0.8635620383E+00f)}
x11{mode=mult trendma=13 seasonalma=s3x5 save=(d11 d12)}
check{save=(acf)}
FrImp01
Seats input:
D=1,BD=1,P=0,BP=0,Q=1,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=2,
TH(1)=-0.469437,
BTH(1)=-0.742854,
TRAMO=-1,BLQT=26.281439,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(2 1 2)(0 1 1)
ar=(-0.3790070744E-01f
0.2054644806E+00f)
ma=( 0.4158746446E+00f
0.2081458431E+00f
0.7489245721E+00f)}
x11{mode=mult trendma=13 seasonalma=s3x5 save=(d11 d12)}
check{save=(acf)}
36
FrImp02
Seats input:
D=1,BD=1,P=0,BP=0,Q=1,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=2,
TH(1)=-0.519174,
BTH(1)=-0.814682,
TRAMO=-1,BLQT=26.025157,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(0 1 2)(0 1 1)
ma=( 0.5107649806E+00f
0.1405083626E-01f
0.8219543211E+00f)}
x11{mode=mult trendma=13 seasonalma=s3x5 save=(d11 d12)}
check{save=(acf)}
FrImp03
Seats input:
D=1,BD=1,P=0,BP=0,Q=1,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=2,
TH(1)=-0.358081,
BTH(1)=-0.937180,
TRAMO=-1,BLQT=18.781023,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(0 1 1) (0 1 1)
ma=( 0.3603913654E+00f
0.9991202971E+00f)}
x11{mode=mult trendma=13 seasonalma=s3x5 save=(d11 d12)}
check{save=(acf)}
FrImp04
Seats input:
D=1,BD=1,P=0,BP=0,Q=1,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=2,
TH(1)=-0.597559,
BTH(1)=-0.833972,
TRAMO=-1,BLQT=25.785357,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(2 1 0)(0 1 1)
ar=(-0.6170016810E+00f
-0.2754927696E+00f)
ma=( 0.8087940547E+00f)}
x11{mode=mult trendma=23 seasonalma=s3x5 save=(d11 d12)}
check{save=(acf)}
FrImp05
Seats input:
D=1,BD=1,P=1,BP=0,Q=0,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=2,
PHI(1)=0.580016,
BTH(1)=-0.819570,
TRAMO=-1,BLQT=16.770111,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
37
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(2 1 0)(0 1 1)
ar=(-0.7015689375E+00f
-0.2035230056E+00f)
ma=( 0.8312610341E+00f)}
x11{mode=mult trendma=13 seasonalma=s3x5 save=(d11 d12)}
check{save=(acf)}
FrImp06
Seats input:
D=1,BD=1,P=0,BP=0,Q=1,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=2,
TH(1)=-0.496396,
BTH(1)=-0.712429,
TRAMO=-1,BLQT=21.718406,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(2 1 0)(0 1 1)
ar=(-0.5464865572E+00f
-0.2236194447E+00f)
ma=( 0.7096894858E+00f)}
x11{mode=mult trendma=13 seasonalma=s3x5 save=(d11 d12)}
check{save=(acf)}
FrImp07
Seats input:
D=1,BD=1,P=0,BP=0,Q=1,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=2,
TH(1)=-0.626725,
BTH(1)=-0.927222,
TRAMO=-1,BLQT=10.685485,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(0 1 1) (0 1 1)
ma=( 0.6266837511E+00f
0.9260471749E+00f)}
x11{mode=mult trendma=13 seasonalma=s3x9 save=(d11 d12)}
check{save=(acf)}
FrImp08
Seats input:
D=1,BD=1,P=0,BP=0,Q=1,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=2,
TH(1)=-0.473246,
BTH(1)=-0.701354,
TRAMO=-1,BLQT=23.196692,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(2 1 0)(0 1 1)
ar=(-0.4651910337E+00f
-0.9500174616E-01f)
ma=( 0.7022830855E+00f)}
38
x11{mode=mult trendma=13 seasonalma=s3x5 save=(d11 d12)}
check{save=(acf)}
FrImp09
Seats input:
D=1,BD=1,P=0,BP=0,Q=1,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=2,
TH(1)=-0.623627,
BTH(1)=-0.654008,
TRAMO=-1,BLQT=27.272252,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(2 1 0)(0 1 1)
ar=(-0.5352737975E+00f
-0.2403309022E+00f)
ma=( 0.6387507205E+00f)}
x11{mode=mult trendma=13 seasonalma=s3x5 save=(d11 d12)}
check{save=(acf)}
FrImp10
Seats input:
D=1,BD=1,P=0,BP=0,Q=1,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=2,
TH(1)=-0.516122,
BTH(1)=-0.548226,
TRAMO=-1,BLQT=15.851545,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(0 1 2)(0 1 1)
ma=( 0.4877054534E+00f
0.5116658498E-01f
0.5445323535E+00f)}
x11{mode=mult trendma=13 seasonalma=s3x5 save=(d11 d12)}
check{save=(acf)}
FrImp11
Seats input:
D=1,BD=1,P=0,BP=0,Q=1,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=2,
TH(1)=-0.550019,
BTH(1)=-0.562474,
TRAMO=-1,BLQT=17.402828,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(0 1 1)(0 1 1)
ma=( 0.5503492125E+00f
0.5615805274E+00f)}
x11{mode=mult trendma=13 seasonalma=s3x5 save=(d11 d12)}
check{save=(acf)}
FrImp12
Seats input:
D=1,BD=1,P=3,BP=0,Q=0,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=2,
PHI(1)=0.381493,
39
PHI(2)=0.280700,
PHI(3)=0.308912,
BTH(1)=-0.980000,
TRAMO=-1,BLQT=33.808182,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(0 1 1) (0 1 1)
ma=( 0.4771239134E+00f
0.9992253600E+00f)}
x11{mode=mult trendma=13 seasonalma=s3x5 save=(d11 d12)}
check{save=(acf)}
Model orders fixed, model parameters free:
FrExp01
Seats input:
D=1,BD=1,P=0,BP=0,Q=1,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=1,
TH(1)=-0.458662,
BTH(1)=-0.646929,
TRAMO=-1,BLQT=15.573744,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(2 1 2)(0 1 1)
ar=(-0.6146149903E+00
0.2810814997E+00)
ma=(-0.1942233453E+00
0.6335310999E+00
0.6486130414E+00)}
x11{mode=mult save=(d11 d12)}
check{save=(acf)}
FrExp02
Seats input:
D=1,BD=1,P=0,BP=0,Q=1,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=1,
TH(1)=-0.368447,
BTH(1)=-0.601682,
TRAMO=-1,BLQT=18.250837,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(0 1 2)(0 1 1)
ma=( 0.3132496774E+00
0.1165852982E+00
0.6061667409E+00)}
x11{mode=mult save=(d11 d12)}
check{save=(acf)}
FrExp03
Seats input:
D=1,BD=0,P=0,BP=1,Q=1,BQ=0,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=1,
BPHI(1)=-0.201888,
TH(1)=-0.706600,
40
TRAMO=-1,BLQT=21.535236,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(0 1 1) (0 1 1)
x11{mode=mult save=(d11 d12)}
check{save=(acf)}
FrExp04
Seats input:
D=1,BD=1,P=0,BP=0,Q=1,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=1,
TH(1)=-0.774064,
BTH(1)=-0.923241,
TRAMO=-1,BLQT=27.665483,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(2 1 0)(0 1 1)
ar=(-0.7038447493E+00
-0.4339817706E+00)
ma=( 0.8899731440E+00)}
x11{mode=mult save=(d11 d12)}
check{save=(acf)}
FrExp05
Seats input:
D=1,BD=1,P=0,BP=0,Q=1,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=1,
TH(1)=-0.589691,
BTH(1)=-0.652684,
TRAMO=-1,BLQT=15.123951,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(2 1 2)(0 1 1)
ar=( 0.2011812314E+00
-0.2173513383E+00)
ma=( 0.9082461034E+00
-0.4553338938E+00
0.6273839741E+00)}
x11{mode=mult save=(d11 d12)}
check{save=(acf)}
FrExp06
Seats input:
D=1,BD=1,P=2,BP=0,Q=0,BQ=0,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=1,
PHI(1)=0.560617,
PHI(2)=0.304828,
TRAMO=-1,BLQT=26.825666,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(0 1 2)(0 1 1)
ma=( 0.6531437910E+00
41
-0.2369674316E+00
0.2524437642E+00)}
x11{mode=mult save=(d11 d12)}
check{save=(acf)}
FrExp07
Seats input:
D=1,BD=1,P=0,BP=0,Q=1,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=1,
TH(1)=-0.706218,
BTH(1)=-0.648650,
TRAMO=-1,BLQT=8.929244,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(0 1 1)(0 1 1)
ma=( 0.7073814950E+00
0.6534618659E+00)}
x11{mode=mult save=(d11 d12)}
check{save=(acf)}
FrExp08
Seats input:
D=1,BD=1,P=0,BP=0,Q=2,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=1,
TH(1)=-0.933254,
TH(2)=0.372568,
BTH(1)=-0.381034,
TRAMO=-1,BLQT=11.891964,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(0 1 1)(0 1 1)
ma=( 0.7630920875E+00
0.4253977234E+00)}
x11{mode=mult save=(d11 d12)}
check{save=(acf)}
FrExp09
Seats input:
D=1,BD=1,P=0,BP=0,Q=1,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=1,
TH(1)=-0.743045,
BTH(1)=-0.593829,
TRAMO=-1,BLQT=18.527110,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(0 1 1)(0 1 1)
ma=( 0.7449801036E+00
0.5928487864E+00)}
x11{mode=mult save=(d11 d12)}
check{save=(acf)}
FrExp10
Seats input:
D=1,BD=1,P=0,BP=0,Q=1,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=1,
42
TH(1)=-0.696577,
BTH(1)=-0.534302,
TRAMO=-1,BLQT=7.808433,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(0 1 2)(0 1 1)
ma=( 0.6885028428E+00
0.1484695287E-01
0.5331679452E+00)}
x11{mode=mult save=(d11 d12)}
check{save=(acf)}
FrExp11
Seats input:
D=1,BD=1,P=0,BP=0,Q=1,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=1,
TH(1)=-0.543608,
BTH(1)=-0.762261,
TRAMO=-1,BLQT=11.599968,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(0 1 1)(0 1 1)
ma=( 0.5438274305E+00
0.7756838981E+00)}
x11{mode=mult save=(d11 d12)}
check{save=(acf)}
FrExp12
Seats input:
D=1,BD=1,P=1,BP=0,Q=0,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=1,
PHI(1)=0.477178,
BTH(1)=-0.899710,
TRAMO=-1,BLQT=35.070401,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(0 1 1) (0 1 1)}
x11{mode=mult save=(d11 d12)}
check{save=(acf)}
FrImp01
Seats input:
D=1,BD=1,P=0,BP=0,Q=1,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=1,
TH(1)=-0.469437,
BTH(1)=-0.742854,
TRAMO=-1,BLQT=26.281439,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(2 1 2)(0 1 1)
ar=(-0.3790070744E-01
0.2054644806E+00)
43
ma=( 0.4158746446E+00
0.2081458431E+00
0.7489245721E+00)}
x11{mode=mult save=(d11 d12)}
check{save=(acf)}
FrImp02
Seats input:
D=1,BD=1,P=0,BP=0,Q=1,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=1,
TH(1)=-0.519174,
BTH(1)=-0.814682,
TRAMO=-1,BLQT=26.025157,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(0 1 2)(0 1 1)
ma=( 0.5107649806E+00
0.1405083626E-01
0.8219543211E+00)}
x11{mode=mult save=(d11 d12)}
check{save=(acf)}
FrImp03
Seats input:
D=1,BD=1,P=0,BP=0,Q=1,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=1,
TH(1)=-0.358081,
BTH(1)=-0.937180,
TRAMO=-1,BLQT=18.781023,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(0 1 1) (0 1 1)}
x11{mode=mult save=(d11 d12)}
check{save=(acf)}
FrImp04
Seats input:
D=1,BD=1,P=0,BP=0,Q=1,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=1,
TH(1)=-0.597559,
BTH(1)=-0.833972,
TRAMO=-1,BLQT=25.785357,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(2 1 0)(0 1 1)
ar=(-0.6170016810E+00
-0.2754927696E+00)
ma=( 0.8087940547E+00)}
x11{mode=mult save=(d11 d12)}
check{save=(acf)}
FrImp05
Seats input:
D=1,BD=1,P=1,BP=0,Q=0,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=1,
44
PHI(1)=0.580016,
BTH(1)=-0.819570,
TRAMO=-1,BLQT=16.770111,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(2 1 0)(0 1 1)
ar=(-0.7015689375E+00
-0.2035230056E+00)
ma=( 0.8312610341E+00)}
x11{mode=mult save=(d11 d12)}
check{save=(acf)}
FrImp06
Seats input:
D=1,BD=1,P=0,BP=0,Q=1,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=1,
TH(1)=-0.496396,
BTH(1)=-0.712429,
TRAMO=-1,BLQT=21.718406,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(2 1 0)(0 1 1)
ar=(-0.5464865572E+00
-0.2236194447E+00)
ma=( 0.7096894858E+00)}
x11{mode=mult save=(d11 d12)}
check{save=(acf)}
FrImp07
Seats input:
D=1,BD=1,P=0,BP=0,Q=1,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=1,
TH(1)=-0.626725,
BTH(1)=-0.927222,
TRAMO=-1,BLQT=10.685485,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(0 1 1) (0 1 1)}
x11{mode=mult save=(d11 d12)}
check{save=(acf)}
FrImp08
Seats input:
D=1,BD=1,P=0,BP=0,Q=1,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=1,
TH(1)=-0.473246,
BTH(1)=-0.701354,
TRAMO=-1,BLQT=23.196692,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(2 1 0)(0 1 1)
ar=(-0.4651910337E+00
45
-0.9500174616E-01)
ma=( 0.7022830855E+00)}
x11{mode=mult save=(d11 d12)}
check{save=(acf)}
FrImp09
Seats input:
D=1,BD=1,P=0,BP=0,Q=1,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=1,
TH(1)=-0.623627,
BTH(1)=-0.654008,
TRAMO=-1,BLQT=27.272252,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(2 1 0)(0 1 1)
ar=(-0.5352737975E+00
-0.2403309022E+00)
ma=( 0.6387507205E+00)}
x11{mode=mult save=(d11 d12)}
check{save=(acf)}
FrImp10
Seats input:
D=1,BD=1,P=0,BP=0,Q=1,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=1,
TH(1)=-0.516122,
BTH(1)=-0.548226,
TRAMO=-1,BLQT=15.851545,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(0 1 2)(0 1 1)
ma=( 0.4877054534E+00
0.5116658498E-01
0.5445323535E+00)}
x11{mode=mult save=(d11 d12)}
check{save=(acf)}
FrImp11
Seats input:
D=1,BD=1,P=0,BP=0,Q=1,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=1,
TH(1)=-0.550019,
BTH(1)=-0.562474,
TRAMO=-1,BLQT=17.402828,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(0 1 1)(0 1 1)
ma=( 0.5503492125E+00
0.5615805274E+00)}
x11{mode=mult save=(d11 d12)}
check{save=(acf)}
FrImp12
Seats input:
D=1,BD=1,P=3,BP=0,Q=0,BQ=1,
46
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=1,
PHI(1)=0.381493,
PHI(2)=0.280700,
PHI(3)=0.308912,
BTH(1)=-0.980000,
TRAMO=-1,BLQT=33.808182,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(0 1 1) (0 1 1)}
x11{mode=mult save=(d11 d12)}
check{save=(acf)}
Model orders free:
For all 24 time series (and all revisions)
Seats input:
lam=-1,interp=1,noadmiss=1,bias=0,imean=0,seats=2,inic=3,idif=3,
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
automdl{method=best file=’x12a.mdl’}
x11{mode=mult/add save=(d11 d12)}
check{save=(acf)}
Remark: mult/add decomposition depends on the result of the first automatic
adjustment by Tramo
Model parameters fixed, X-11: 13-term Henderson filter:
FrExp04
Seats input:
D=1,BD=1,P=0,BP=0,Q=1,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=2,
TH(1)=-0.774068,
BTH(1)=-0.923260,
TRAMO=-1,BLQT=27.665645,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(2 1 0)(0 1 1)
ar=(-0.7038447493E+00f
-0.4339817706E+00f)
ma=( 0.8899731440E+00f)}
x11{mode=mult trendma=13 seasonalma=s3x5 save=(d11 d12)}
check{save=(acf)}
Model parameters fixed, X-11: 23-term Henderson filter:
FrExp04
Seats input:
D=1,BD=1,P=0,BP=0,Q=1,BQ=1,
LAM=0,IMEAN=0,PG=1,MQ=12,MODEL=0,INIT=2,
TH(1)=-0.774068,
BTH(1)=-0.923260,
TRAMO=-1,BLQT=27.665645,HS=1.500000,CRMEAN=0,EPSPHI=2.000000,
OUT=0,RSA=0,QMAX=50,NOADMISS=1,BIAS=0,
47
SMTR=0,THTR=-0.400000,RMOD=0.500000,MAXBIAS=0.500000,IQM=24
X-12-Arima input:
transform{function=log}
estimate{save=(model)}
arima{model=(2 1 0)(0 1 1)
ar=(-0.7038447493E+00f
-0.4339817706E+00f)
ma=( 0.8899731440E+00f)}
x11{mode=mult trendma=23 seasonalma=s3x5 save=(d11 d12)}
check{save=(acf)}
Explanation of the time series used:
24 series of the French external trade, nomenclature Nec 2, export and import,
monthly data:
Frexp##: French export
Frimp##: French import
##:
01: Agriculture
07: Professional equipment
02: Food products
08: Electrical machinery and apparatus
03: Energy
09: Cars for households
04: Mineral goods
10: Car spare parts, commercial vehicles
05: Metallic products
11: Consumer goods
06: Non-metallic intermediate goods 12: Other goods
starting date:
January 1980
ending date:
December 1994
length:
180 observations