estTSFmodel: Estimate Time Series Factor Model
In tsfa: Time Series Factor Analysis
Description
Usage
Arguments
Details
Value
Author(s)
References
See Also
Examples
Description
Estimate a TSFmodel.
Usage
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estTSFmodel(y, p, diff.=TRUE,
est="factanal",
estArgs=list(scores="none", control=list(opt=list(maxit=10000))),
rotation=if(p==1) "none" else "quartimin",
rotationArgs=NULL,
GPFargs=list(Tmat=diag(p),normalize=TRUE, eps=1e-5, maxit=1000),
BpermuteTarget=NULL,
factorNames=paste("Factor", seq(p)))
estTSF.ML(y, p, diff.=TRUE,
rotation=if(p==1) "none" else "quartimin",
rotationArgs=NULL,
normalize=TRUE, eps=1e-5, maxit=1000, Tmat=diag(p),
BpermuteTarget=NULL,
factorNames=paste("Factor", seq(p)))
Arguments
y
a time series matrix.
p
integer indication number of factors to estimate.
diff.
logical indicating if model should be estimated with
differenced data.
est
character vector indicating the factor
estimation method (currently only factanal is supported).
estArgs
list passed to as arguments to the estimation function.
rotation
character vector indicating the factor
rotation method (see GPArotation for options).
rotationArgs
list passed to the rotation method,
specifying arguments for the rotation criteria.
GPFargs
list passed to GPFoblq or GPForth, possibly via
the rotation method, specifying arguments for the rotation
optimization. See GPFoblq and GPForth.
normalize
Passed to GPFoblq. TRUE means do Kaiser normalization before
rotation and then undo it after completing rotatation. FALSE means do
no normalization. See GPFoblq for other possibilities.
eps
passed to GPFoblq
maxit
passed to GPFoblq
Tmat
passed to GPFoblq
BpermuteTarget
matrix of loadings. If supplied, this is used to permute the
order of estimated factors and change signs in order to
compare properly.
factorNames
vector of strings indicating names to be given to factor
series.
Details
The function estTSF.ML is a wrapper to estTSFmodel.
The function estTSF.ML estimates parameters using standard
(quasi) ML factor analysis (on the correlation matrix and then scaled back).
The function factanal with no rotation is used to find the initial
(orthogonal) solution. Rotation, if specified, is then done
with GPFoblq.
factanal always uses the correlation matrix, so standardizing does
not affect the solution.
If diff. is TRUE (the default) the indicator data is differenced
before it is passed to factanal. This is necessary if the data is not
stationary. The resulting Bartlett factor score coefficient matrix (rotated)
is applied to the undifferenced data. See Gilbert and Meijer (2005) for a
discussion of this approach.
If rotation is "none" the result of the factanal
estimation is not rotated. In this case, to avoid confusion with a rotated
solution, the factor covariance matrix Phi is returned as NULL.
Another possibility for its value would be the identity matrix, but this is
not calculated so NULL avoids confusion.
The arguments rotation, methodArgs, normalize,
eps, maxit, and Tmat are passed to
GPFoblq.
The estimated loadings, Bartlett factor score coefficient matrix and
predicted factor scores
are put in a TSFmodel which is part of the returned object.
The Bartlett factor score coefficient matrix can be calculated as
(B' Omega exp(-1) B) exp(-1) B' Omega exp(-1) x
or equivalently as
(B' Sigma exp(-1) B) exp(-1) B' Sigma exp(-1) x
The first is simpler because Omega is diagonal, but breaks down
with a Heywood case, because Omega is then singular (one or
more of its diagonal elements are zero). The second only requires
nonsingularity of Sigma. Typically, Sigma is not singular
even if Omega is singular.
Sigma is calculated from B Phi B' + Omega,
where B, Phi, and Omega are the
estimated values returned from factanal and rotated.
The data covariance could also be used for Sigma.
(It returns the same result with this estimation method.)
The returned TSFestModel object is a list containing
- model
the estimated TSFmodel.
- data
the indicator data used in the estimation.
- estimates
a list of
- estimation
a character string indicating the name of the
estimation function.
- diff.
the setting of the argument diff.
- rotation
the setting of the argument rotation.
- uniquenesses
the estimated uniquenesses.
- BpermuteTarget
the setting of the argument BpermuteTarget.
Value
A TSFestModel object which is a list containing TSFmodel,
the data, and some information about the estimation.
Author(s)
Paul Gilbert and Erik Meijer
References
Gilbert, Paul D. and Meijer, Erik (2005)
Time Series Factor Analaysis with an Application to Measuring Money.
Research Report 05F10, University of Groningen, SOM Research School.
Available from https://hdl.handle.net/11370/d7d4ea3d-af1d-487a-b9b6-c0816994ef5a.
See Also
TSFmodel,
GPFoblq,
rotations,
factanal
Examples
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if (require("CDNmoney")){
data("CanadianMoneyData.asof.28Jan2005", package="CDNmoney")
data("CanadianCreditData.asof.28Jan2005", package="CDNmoney")
z <- tframed(tbind(
MB2001,
MB486 + MB452 + MB453 ,
NonbankCheq,
MB472 + MB473 + MB487p,
MB475,
NonbankNonCheq + MB454 + NonbankTerm + MB2046 + MB2047 + MB2048 +
MB2057 + MB2058 + MB482),
names=c("currency", "personal cheq.", "NonbankCheq",
"N-P demand & notice", "N-P term", "Investment" )
)
z <- tfwindow(tbind (z, ConsumerCredit, ResidentialMortgage,
ShortTermBusinessCredit, OtherBusinessCredit),
start=c(1981,11), end=c(2004,11))
cpi <- 100 * M1total / M1real
popm <- M1total / M1PerCapita
scale <- tfwindow(1e8 /(popm * cpi), tf=tframe(z))
MBandCredit <- sweep(z, 1, scale, "*")
c4withML <- estTSF.ML(MBandCredit, 4)
tfplot(ytoypc(factors(c4withML)),
Title="Factors from 4 factor model (year-to-year growth rate)")
tfplot(c4withML, graphs.per.page=3)
summary(c4withML)
summary(TSFmodel(c4withML))
}
Example output
Loading required package: GPArotation
Loading required package: dse
Loading required package: tfplot
Loading required package: tframe
Attaching package: 'dse'
The following objects are masked from 'package:stats':
acf, simulate
Loading required package: EvalEst
Loading required package: CDNmoney
factors have 277 observations from: 1981 11 to 2004 11
Estimated loadings:
NULL
Standardized (using differenced data covariance):
Factor 1 Factor 2 Factor 3 Factor 4
currency 1.01983211 0.09441862 0.09386876 0.08001695
personal cheq. -0.02898840 0.20319639 -0.87632955 0.07894600
NonbankCheq 0.20214387 -0.13884613 -0.36792951 -0.11966332
N-P demand & notice 0.55851463 -0.00326414 -0.20169780 -0.24090075
N-P term 0.02120284 0.10107575 0.23481508 -0.33307726
Investment 0.15013102 0.45888993 0.23944032 -0.06862474
Consumer Credit 0.01841197 0.10508972 -0.10142580 -0.79551987
Residential Mortgage 0.21597515 0.49350633 -0.22622020 -0.14854196
Short Term Business Credit -0.09041731 0.23970572 0.01376311 -0.09703765
Other Business Credit 0.09632589 0.66331904 -0.23994908 -0.04224045
Mean of data:
Series 1 Series 2 Series 3 Series 4 Series 5 Series 6 Series 7
explained 813.991331 4269.2896 78.4043 3126.973 4077.171 15390.097 4052.2894
actual 819.909058 4151.6513 539.9685 1902.856 2319.560 16637.501 4154.8935
error -5.917727 117.6383 -461.5642 1224.117 1757.612 -1247.404 -102.6041
Series 8 Series 9 Series 10
explained 9185.9445 5376.997 11974.7940
actual 9909.9751 7568.010 11222.5148
error -724.0306 -2191.013 752.2792
Mean of differenced data:
Series 1 Series 2 Series 3 Series 4 Series 5 Series 6
explained 1.47595493 6.753944 -0.3051294 7.062696 15.997702 46.541336
actual 1.39838537 2.880048 3.1577833 9.156883 4.926683 48.744141
error 0.07756956 3.873897 -3.4629128 -2.094187 11.071019 -2.202805
Series 7 Series 8 Series 9 Series 10
explained 13.3599344 24.335148 16.322258 31.695674
actual 12.7034230 29.878367 -8.066348 37.283246
error 0.6565114 -5.543219 24.388606 -5.587572
Mean of factors:
Factor 1 Factor 2 Factor 3 Factor 4
48.21825 283.91583 -60.31811 -123.47407
Mean of differenced factors:
Factor 1 Factor 2 Factor 3 Factor 4
0.07240118 0.79590893 -0.03766539 -0.44814674
Fit statistics:
chisq df pval delta RMSEA RNI
17.84348219 11.00000000 0.08528416 6.84348219 0.04747748 0.98988468
CFI MCI GFI AGFI AIC CAIC
0.98988468 0.98767892 0.98812338 0.94061689 -4.15651781 309.14112028
SIC CAK CK
265.14112028 0.38349088 0.39672577
tsfa documentation built on Jan. 13, 2021, 10:53 a.m.
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Description Usage Arguments Details Value Author(s) References See Also Examples
Description
Estimate a TSFmodel.
Usage
1 2 3 4 5 6 7 8 9 10 11 12 13 14 | estTSFmodel(y, p, diff.=TRUE,
est="factanal",
estArgs=list(scores="none", control=list(opt=list(maxit=10000))),
rotation=if(p==1) "none" else "quartimin",
rotationArgs=NULL,
GPFargs=list(Tmat=diag(p),normalize=TRUE, eps=1e-5, maxit=1000),
BpermuteTarget=NULL,
factorNames=paste("Factor", seq(p)))
estTSF.ML(y, p, diff.=TRUE,
rotation=if(p==1) "none" else "quartimin",
rotationArgs=NULL,
normalize=TRUE, eps=1e-5, maxit=1000, Tmat=diag(p),
BpermuteTarget=NULL,
factorNames=paste("Factor", seq(p)))
|
Arguments
y |
a time series matrix. |
p |
integer indication number of factors to estimate. |
diff. |
logical indicating if model should be estimated with differenced data. |
est |
character vector indicating the factor estimation method (currently only factanal is supported). |
estArgs |
list passed to as arguments to the estimation function. |
rotation |
character vector indicating the factor rotation method (see GPArotation for options). |
rotationArgs |
list passed to the rotation method, specifying arguments for the rotation criteria. |
GPFargs |
list passed to |
normalize |
Passed to |
eps |
passed to |
maxit |
passed to |
Tmat |
passed to |
BpermuteTarget |
matrix of loadings. If supplied, this is used to permute the order of estimated factors and change signs in order to compare properly. |
factorNames |
vector of strings indicating names to be given to factor series. |
Details
The function estTSF.ML is a wrapper to estTSFmodel.
The function estTSF.ML estimates parameters using standard
(quasi) ML factor analysis (on the correlation matrix and then scaled back).
The function factanal with no rotation is used to find the initial
(orthogonal) solution. Rotation, if specified, is then done
with GPFoblq.
factanal always uses the correlation matrix, so standardizing does
not affect the solution.
If diff. is TRUE (the default) the indicator data is differenced
before it is passed to factanal. This is necessary if the data is not
stationary. The resulting Bartlett factor score coefficient matrix (rotated)
is applied to the undifferenced data. See Gilbert and Meijer (2005) for a
discussion of this approach.
If rotation is "none" the result of the factanal
estimation is not rotated. In this case, to avoid confusion with a rotated
solution, the factor covariance matrix Phi is returned as NULL.
Another possibility for its value would be the identity matrix, but this is
not calculated so NULL avoids confusion.
The arguments rotation, methodArgs, normalize,
eps, maxit, and Tmat are passed to
GPFoblq.
The estimated loadings, Bartlett factor score coefficient matrix and
predicted factor scores
are put in a TSFmodel which is part of the returned object.
The Bartlett factor score coefficient matrix can be calculated as
(B' Omega exp(-1) B) exp(-1) B' Omega exp(-1) x
or equivalently as
(B' Sigma exp(-1) B) exp(-1) B' Sigma exp(-1) x
The first is simpler because Omega is diagonal, but breaks down
with a Heywood case, because Omega is then singular (one or
more of its diagonal elements are zero). The second only requires
nonsingularity of Sigma. Typically, Sigma is not singular
even if Omega is singular.
Sigma is calculated from B Phi B' + Omega,
where B, Phi, and Omega are the
estimated values returned from factanal and rotated.
The data covariance could also be used for Sigma.
(It returns the same result with this estimation method.)
The returned TSFestModel object is a list containing
- model
the estimated
TSFmodel.- data
the indicator data used in the estimation.
- estimates
a list of
- estimation
a character string indicating the name of the estimation function.
- diff.
the setting of the argument
diff.- rotation
the setting of the argument
rotation.- uniquenesses
the estimated uniquenesses.
- BpermuteTarget
the setting of the argument
BpermuteTarget.
Value
A TSFestModel object which is a list containing TSFmodel,
the data, and some information about the estimation.
Author(s)
Paul Gilbert and Erik Meijer
References
Gilbert, Paul D. and Meijer, Erik (2005) Time Series Factor Analaysis with an Application to Measuring Money. Research Report 05F10, University of Groningen, SOM Research School. Available from https://hdl.handle.net/11370/d7d4ea3d-af1d-487a-b9b6-c0816994ef5a.
See Also
TSFmodel,
GPFoblq,
rotations,
factanal
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 | if (require("CDNmoney")){
data("CanadianMoneyData.asof.28Jan2005", package="CDNmoney")
data("CanadianCreditData.asof.28Jan2005", package="CDNmoney")
z <- tframed(tbind(
MB2001,
MB486 + MB452 + MB453 ,
NonbankCheq,
MB472 + MB473 + MB487p,
MB475,
NonbankNonCheq + MB454 + NonbankTerm + MB2046 + MB2047 + MB2048 +
MB2057 + MB2058 + MB482),
names=c("currency", "personal cheq.", "NonbankCheq",
"N-P demand & notice", "N-P term", "Investment" )
)
z <- tfwindow(tbind (z, ConsumerCredit, ResidentialMortgage,
ShortTermBusinessCredit, OtherBusinessCredit),
start=c(1981,11), end=c(2004,11))
cpi <- 100 * M1total / M1real
popm <- M1total / M1PerCapita
scale <- tfwindow(1e8 /(popm * cpi), tf=tframe(z))
MBandCredit <- sweep(z, 1, scale, "*")
c4withML <- estTSF.ML(MBandCredit, 4)
tfplot(ytoypc(factors(c4withML)),
Title="Factors from 4 factor model (year-to-year growth rate)")
tfplot(c4withML, graphs.per.page=3)
summary(c4withML)
summary(TSFmodel(c4withML))
}
|
Example output
Loading required package: GPArotation
Loading required package: dse
Loading required package: tfplot
Loading required package: tframe
Attaching package: 'dse'
The following objects are masked from 'package:stats':
acf, simulate
Loading required package: EvalEst
Loading required package: CDNmoney
factors have 277 observations from: 1981 11 to 2004 11
Estimated loadings:
NULL
Standardized (using differenced data covariance):
Factor 1 Factor 2 Factor 3 Factor 4
currency 1.01983211 0.09441862 0.09386876 0.08001695
personal cheq. -0.02898840 0.20319639 -0.87632955 0.07894600
NonbankCheq 0.20214387 -0.13884613 -0.36792951 -0.11966332
N-P demand & notice 0.55851463 -0.00326414 -0.20169780 -0.24090075
N-P term 0.02120284 0.10107575 0.23481508 -0.33307726
Investment 0.15013102 0.45888993 0.23944032 -0.06862474
Consumer Credit 0.01841197 0.10508972 -0.10142580 -0.79551987
Residential Mortgage 0.21597515 0.49350633 -0.22622020 -0.14854196
Short Term Business Credit -0.09041731 0.23970572 0.01376311 -0.09703765
Other Business Credit 0.09632589 0.66331904 -0.23994908 -0.04224045
Mean of data:
Series 1 Series 2 Series 3 Series 4 Series 5 Series 6 Series 7
explained 813.991331 4269.2896 78.4043 3126.973 4077.171 15390.097 4052.2894
actual 819.909058 4151.6513 539.9685 1902.856 2319.560 16637.501 4154.8935
error -5.917727 117.6383 -461.5642 1224.117 1757.612 -1247.404 -102.6041
Series 8 Series 9 Series 10
explained 9185.9445 5376.997 11974.7940
actual 9909.9751 7568.010 11222.5148
error -724.0306 -2191.013 752.2792
Mean of differenced data:
Series 1 Series 2 Series 3 Series 4 Series 5 Series 6
explained 1.47595493 6.753944 -0.3051294 7.062696 15.997702 46.541336
actual 1.39838537 2.880048 3.1577833 9.156883 4.926683 48.744141
error 0.07756956 3.873897 -3.4629128 -2.094187 11.071019 -2.202805
Series 7 Series 8 Series 9 Series 10
explained 13.3599344 24.335148 16.322258 31.695674
actual 12.7034230 29.878367 -8.066348 37.283246
error 0.6565114 -5.543219 24.388606 -5.587572
Mean of factors:
Factor 1 Factor 2 Factor 3 Factor 4
48.21825 283.91583 -60.31811 -123.47407
Mean of differenced factors:
Factor 1 Factor 2 Factor 3 Factor 4
0.07240118 0.79590893 -0.03766539 -0.44814674
Fit statistics:
chisq df pval delta RMSEA RNI
17.84348219 11.00000000 0.08528416 6.84348219 0.04747748 0.98988468
CFI MCI GFI AGFI AIC CAIC
0.98988468 0.98767892 0.98812338 0.94061689 -4.15651781 309.14112028
SIC CAK CK
265.14112028 0.38349088 0.39672577
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