Ajour du GMM régulier
This commit is contained in:
François Pelletier
parent
42b17db119
commit
9cb92e4e50
3 changed files with 207 additions and 12 deletions
|
|
@ -46,6 +46,8 @@ alpha.confint <- 0.05
|
|||
alpha.test <- 0.05
|
||||
#Chargement des données
|
||||
RETURNS <- head(read.csv("abbeyn.csv",sep="\t",header=TRUE)[,1],-1)
|
||||
#Taille de l'échantillon
|
||||
n <- length(RETURNS)
|
||||
@
|
||||
|
||||
\section{Test de normalité}
|
||||
|
|
@ -60,7 +62,7 @@ EppsPulley.test(RETURNS)
|
|||
scaledRETURNS <- as.vector(scale(RETURNS))
|
||||
@
|
||||
|
||||
\section{Estimation}
|
||||
\section{Première estimation par QEE}
|
||||
|
||||
<<>>=
|
||||
## Point de départ
|
||||
|
|
@ -68,14 +70,79 @@ pt.depart <- startparamGAL(scaledRETURNS)
|
|||
## Fonctions pour les moments
|
||||
meanQEE <- function(param) mGAL(param,1)
|
||||
varianceQEE <- function(param) cmGAL(param,2)
|
||||
sdGEE <- function(param) sqrt(cmGAL(param,2))
|
||||
skewnessGEE <- function(param) cmGAL(param,3)
|
||||
kurtosisGEE <- function(param) cmGAL(param,4)
|
||||
sdQEE <- function(param) sqrt(cmGAL(param,2))
|
||||
skewnessQEE <- function(param) cmGAL(param,3)
|
||||
kurtosisQEE <- function(param) cmGAL(param,4)
|
||||
## Fonctions pour les dérivées
|
||||
dmeanQEE <- function(param) dmGAL(param,1)
|
||||
dsdGEE <- function(param) dmGAL(param,2)
|
||||
dsdQEE <- function(param) dmGAL(param,2)
|
||||
## Estimation gaussienne
|
||||
optim1 <- optim(pt.depart,obj.gauss,gr=NULL,scaledRETURNS,meanQEE,varianceQEE,dmeanQEE,dsdGEE)
|
||||
optim1 <- optim(pt.depart,obj.gauss,gr=NULL,scaledRETURNS,meanQEE,varianceQEE,dmeanQEE,dsdQEE)
|
||||
pt.optim1 <- optim1$par
|
||||
## Estimation de crowder
|
||||
optim2 <- optim(pt.depart,obj.Crowder,gr=NULL,scaledRETURNS,meanQEE,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE)
|
||||
pt.optim2 <- optim2$par
|
||||
## Estimation de crowder modifiée
|
||||
optim3 <- optim(pt.depart,obj.Crowder.Mod,gr=NULL,scaledRETURNS,meanQEE,varianceQEE,dmeanQEE,dsdQEE)
|
||||
pt.optim3 <- optim3$par
|
||||
@
|
||||
|
||||
\section{Résultats de la première estimation par QEE}
|
||||
|
||||
<<>>=
|
||||
cov.optim1 <- covariance.QEE(M.gauss(pt.optim1,scaledRETURNS,meanQEE,varianceQEE,dmeanQEE,dsdQEE),
|
||||
V.gauss(pt.optim1,scaledRETURNS,meanQEE,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),n)
|
||||
cov.optim2 <- covariance.QEE(M.Crowder(pt.optim2,scaledRETURNS,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),
|
||||
V.Crowder(pt.optim2,scaledRETURNS,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),n)
|
||||
cov.optim3 <- covariance.QEE(M.Crowder.Mod(pt.optim3,scaledRETURNS,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),
|
||||
V.Crowder.Mod(pt.optim3,scaledRETURNS,varianceQEE,dmeanQEE,dsdQEE),n)
|
||||
confidence.interval.QEE(pt.optim1,cov.optim1,n)
|
||||
confidence.interval.QEE(pt.optim2,cov.optim2,n)
|
||||
confidence.interval.QEE(pt.optim3,cov.optim3,n)
|
||||
@
|
||||
|
||||
\section{Seconde estimation par QEE}
|
||||
|
||||
<<>>=
|
||||
## Estimation gaussienne
|
||||
optim4 <- optim(pt.optim1,obj.gauss,gr=NULL,scaledRETURNS,meanQEE,varianceQEE,dmeanQEE,dsdQEE,
|
||||
ginv(V.gauss(pt.optim1,scaledRETURNS,meanQEE,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE)))
|
||||
pt.optim4 <- optim4$par
|
||||
## Estimation de crowder
|
||||
optim5 <- optim(pt.optim2,obj.Crowder,gr=NULL,scaledRETURNS,meanQEE,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE,
|
||||
ginv(V.Crowder(pt.optim2,scaledRETURNS,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE)))
|
||||
pt.optim5 <- optim5$par
|
||||
## Estimation de crowder modifiée
|
||||
optim6 <- optim(pt.optim3,obj.Crowder.Mod,gr=NULL,scaledRETURNS,meanQEE,varianceQEE,dmeanQEE,dsdQEE,
|
||||
ginv(V.Crowder.Mod(pt.optim3,scaledRETURNS,varianceQEE,dmeanQEE,dsdQEE)))
|
||||
pt.optim6 <- optim6$par
|
||||
@
|
||||
|
||||
\section{Résultats de la seconde estimation par QEE}
|
||||
|
||||
<<>>=
|
||||
cov.optim4 <- covariance.QEE(M.gauss(pt.optim4,scaledRETURNS,meanQEE,varianceQEE,dmeanQEE,dsdQEE),
|
||||
V.gauss(pt.optim4,scaledRETURNS,meanQEE,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),n)
|
||||
cov.optim5 <- covariance.QEE(M.Crowder(pt.optim5,scaledRETURNS,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),
|
||||
V.Crowder(pt.optim5,scaledRETURNS,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),n)
|
||||
cov.optim6 <- covariance.QEE(M.Crowder.Mod(pt.optim6,scaledRETURNS,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),
|
||||
V.Crowder.Mod(pt.optim6,scaledRETURNS,varianceQEE,dmeanQEE,dsdQEE),n)
|
||||
confidence.interval.QEE(pt.optim4,cov.optim4,n)
|
||||
confidence.interval.QEE(pt.optim5,cov.optim5,n)
|
||||
confidence.interval.QEE(pt.optim6,cov.optim6,n)
|
||||
@
|
||||
|
||||
\section{Estimation par GMM}
|
||||
|
||||
<<>>=
|
||||
## GMM régulier
|
||||
optim7 <- optim.GMM(pt.depart,conditions.vector=meanvariance.gmm.vector,data=scaledRETURNS,W=diag(2),
|
||||
meanf=meanQEE,variancef=varianceQEE)
|
||||
|
||||
## GMM itératif
|
||||
optim8 <- iterative.GMM(pt.depart,conditions.vector=meanvariance.gmm.vector,data=scaledRETURNS,W=diag(2),
|
||||
meanf=meanQEE,variancef=varianceQEE)
|
||||
@
|
||||
|
||||
|
||||
\end{document}
|
||||
|
|
|
|||
BIN
GAL-Buckle95.pdf
BIN
GAL-Buckle95.pdf
Binary file not shown.
140
GAL-Buckle95.tex
140
GAL-Buckle95.tex
|
|
@ -49,6 +49,8 @@
|
|||
> alpha.test <- 0.05
|
||||
> #Chargement des données
|
||||
> RETURNS <- head(read.csv("abbeyn.csv",sep="\t",header=TRUE)[,1],-1)
|
||||
> #Taille de l'échantillon
|
||||
> n <- length(RETURNS)
|
||||
\end{Sinput}
|
||||
\end{Schunk}
|
||||
|
||||
|
|
@ -90,7 +92,7 @@ $Reject
|
|||
\end{Sinput}
|
||||
\end{Schunk}
|
||||
|
||||
\section{Estimation}
|
||||
\section{Première estimation par QEE}
|
||||
|
||||
\begin{Schunk}
|
||||
\begin{Sinput}
|
||||
|
|
@ -99,11 +101,137 @@ $Reject
|
|||
> ## Fonctions pour les moments
|
||||
> meanQEE <- function(param) mGAL(param,1)
|
||||
> varianceQEE <- function(param) cmGAL(param,2)
|
||||
> sdGEE <- function(param) sqrt(cmGAL(param,2))
|
||||
> skewnessGEE <- function(param) cmGAL(param,3)
|
||||
> kurtosisGEE <- function(param) cmGAL(param,4)
|
||||
> sdQEE <- function(param) sqrt(cmGAL(param,2))
|
||||
> skewnessQEE <- function(param) cmGAL(param,3)
|
||||
> kurtosisQEE <- function(param) cmGAL(param,4)
|
||||
> ## Fonctions pour les dérivées
|
||||
> dmeanQEE <- function(param) dmGAL(param,1)
|
||||
> dsdGEE <- function(param) dmGAL(param,2)
|
||||
> dsdQEE <- function(param) dmGAL(param,2)
|
||||
> ## Estimation gaussienne
|
||||
> optim1 <- optim(pt.depart,obj.gauss,scaledRETURNS,meanQEE,varianceQEE,dmeanQEE,dsdGEE)
|
||||
> optim1 <- optim(pt.depart,obj.gauss,gr=NULL,scaledRETURNS,meanQEE,varianceQEE,dmeanQEE,dsdQEE)
|
||||
> pt.optim1 <- optim1$par
|
||||
> ## Estimation de crowder
|
||||
> optim2 <- optim(pt.depart,obj.Crowder,gr=NULL,scaledRETURNS,meanQEE,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE)
|
||||
> pt.optim2 <- optim2$par
|
||||
> ## Estimation de crowder modifiée
|
||||
> optim3 <- optim(pt.depart,obj.Crowder.Mod,gr=NULL,scaledRETURNS,meanQEE,varianceQEE,dmeanQEE,dsdQEE)
|
||||
> pt.optim3 <- optim3$par
|
||||
\end{Sinput}
|
||||
\end{Schunk}
|
||||
|
||||
\section{Résultats de la première estimation par QEE}
|
||||
|
||||
\begin{Schunk}
|
||||
\begin{Sinput}
|
||||
> cov.optim1 <- covariance.QEE(M.gauss(pt.optim1,scaledRETURNS,meanQEE,varianceQEE,dmeanQEE,dsdQEE),
|
||||
+ V.gauss(pt.optim1,scaledRETURNS,meanQEE,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),n)
|
||||
> cov.optim2 <- covariance.QEE(M.Crowder(pt.optim2,scaledRETURNS,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),
|
||||
+ V.Crowder(pt.optim2,scaledRETURNS,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),n)
|
||||
> cov.optim3 <- covariance.QEE(M.Crowder.Mod(pt.optim3,scaledRETURNS,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),
|
||||
+ V.Crowder.Mod(pt.optim3,scaledRETURNS,varianceQEE,dmeanQEE,dsdQEE),n)
|
||||
> confidence.interval.QEE(pt.optim1,cov.optim1,n)
|
||||
\end{Sinput}
|
||||
\begin{Soutput}
|
||||
LOWER ESTIMATE UPPER
|
||||
[1,] -0.780018 -0.726048 -0.672077
|
||||
[2,] 0.436002 0.596316 0.756630
|
||||
[3,] 0.262650 0.359186 0.455722
|
||||
[4,] 1.994757 2.021370 2.047982
|
||||
\end{Soutput}
|
||||
\begin{Sinput}
|
||||
> confidence.interval.QEE(pt.optim2,cov.optim2,n)
|
||||
\end{Sinput}
|
||||
\begin{Soutput}
|
||||
LOWER ESTIMATE UPPER
|
||||
[1,] -0.694457 -0.627404 -0.560351
|
||||
[2,] 0.413764 0.640292 0.866820
|
||||
[3,] 0.232650 0.334028 0.435405
|
||||
[4,] 1.839966 1.878296 1.916626
|
||||
\end{Soutput}
|
||||
\begin{Sinput}
|
||||
> confidence.interval.QEE(pt.optim3,cov.optim3,n)
|
||||
\end{Sinput}
|
||||
\begin{Soutput}
|
||||
LOWER ESTIMATE UPPER
|
||||
[1,] -0.765288 -0.711439 -0.657589
|
||||
[2,] 0.455485 0.606642 0.757798
|
||||
[3,] 0.264669 0.362932 0.461195
|
||||
[4,] 1.932691 1.960299 1.987906
|
||||
\end{Soutput}
|
||||
\end{Schunk}
|
||||
|
||||
\section{Seconde estimation par QEE}
|
||||
|
||||
\begin{Schunk}
|
||||
\begin{Sinput}
|
||||
> ## Estimation gaussienne
|
||||
> optim4 <- optim(pt.optim1,obj.gauss,gr=NULL,scaledRETURNS,meanQEE,varianceQEE,dmeanQEE,dsdQEE,
|
||||
+ ginv(V.gauss(pt.optim1,scaledRETURNS,meanQEE,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE)))
|
||||
> pt.optim4 <- optim4$par
|
||||
> ## Estimation de crowder
|
||||
> optim5 <- optim(pt.optim2,obj.Crowder,gr=NULL,scaledRETURNS,meanQEE,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE,
|
||||
+ ginv(V.Crowder(pt.optim2,scaledRETURNS,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE)))
|
||||
> pt.optim5 <- optim5$par
|
||||
> ## Estimation de crowder modifiée
|
||||
> optim6 <- optim(pt.optim3,obj.Crowder.Mod,gr=NULL,scaledRETURNS,meanQEE,varianceQEE,dmeanQEE,dsdQEE,
|
||||
+ ginv(V.Crowder.Mod(pt.optim3,scaledRETURNS,varianceQEE,dmeanQEE,dsdQEE)))
|
||||
> pt.optim6 <- optim6$par
|
||||
\end{Sinput}
|
||||
\end{Schunk}
|
||||
|
||||
\section{Résultats de la seconde estimation par QEE}
|
||||
|
||||
\begin{Schunk}
|
||||
\begin{Sinput}
|
||||
> cov.optim4 <- covariance.QEE(M.gauss(pt.optim4,scaledRETURNS,meanQEE,varianceQEE,dmeanQEE,dsdQEE),
|
||||
+ V.gauss(pt.optim4,scaledRETURNS,meanQEE,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),n)
|
||||
> cov.optim5 <- covariance.QEE(M.Crowder(pt.optim5,scaledRETURNS,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),
|
||||
+ V.Crowder(pt.optim5,scaledRETURNS,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),n)
|
||||
> cov.optim6 <- covariance.QEE(M.Crowder.Mod(pt.optim6,scaledRETURNS,varianceQEE,skewnessQEE,kurtosisQEE,dmeanQEE,dsdQEE),
|
||||
+ V.Crowder.Mod(pt.optim6,scaledRETURNS,varianceQEE,dmeanQEE,dsdQEE),n)
|
||||
> confidence.interval.QEE(pt.optim4,cov.optim4,n)
|
||||
\end{Sinput}
|
||||
\begin{Soutput}
|
||||
LOWER ESTIMATE UPPER
|
||||
[1,] -0.779792 -0.725853 -0.671914
|
||||
[2,] 0.436017 0.596319 0.756622
|
||||
[3,] 0.262456 0.358969 0.455482
|
||||
[4,] 1.995452 2.022048 2.048644
|
||||
\end{Soutput}
|
||||
\begin{Sinput}
|
||||
> confidence.interval.QEE(pt.optim5,cov.optim5,n)
|
||||
\end{Sinput}
|
||||
\begin{Soutput}
|
||||
LOWER ESTIMATE UPPER
|
||||
[1,] -0.692712 -0.625874 -0.559036
|
||||
[2,] 0.414139 0.640445 0.866750
|
||||
[3,] 0.231568 0.332845 0.434122
|
||||
[4,] 1.842116 1.880376 1.918636
|
||||
\end{Soutput}
|
||||
\begin{Sinput}
|
||||
> confidence.interval.QEE(pt.optim6,cov.optim6,n)
|
||||
\end{Sinput}
|
||||
\begin{Soutput}
|
||||
LOWER ESTIMATE UPPER
|
||||
[1,] -0.766288 -0.712450 -0.658612
|
||||
[2,] 0.455051 0.606193 0.757334
|
||||
[3,] 0.264972 0.363196 0.461419
|
||||
[4,] 1.934050 1.961614 1.989178
|
||||
\end{Soutput}
|
||||
\end{Schunk}
|
||||
|
||||
\section{Estimation par GMM}
|
||||
|
||||
\begin{Schunk}
|
||||
\begin{Sinput}
|
||||
> ## GMM régulier
|
||||
> optim7 <- optim.GMM(pt.depart,conditions.vector=meanvariance.gmm.vector,data=scaledRETURNS,W=diag(2),
|
||||
+ meanf=meanQEE,variancef=varianceQEE)
|
||||
> ## GMM itératif
|
||||
> optim8 <- iterative.GMM(pt.depart,conditions.vector=meanvariance.gmm.vector,data=scaledRETURNS,W=diag(2),
|
||||
+ meanf=meanQEE,variancef=varianceQEE)
|
||||
\end{Sinput}
|
||||
\end{Schunk}
|
||||
|
||||
|
||||
\end{document}
|
||||
|
|
|
|||
Loading…
Reference in a new issue