\documentclass{report}
\usepackage{Sweave}
\usepackage{graphicx}
\usepackage[francais]{babel} 
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc} 
\usepackage{amsmath} 
\usepackage{amsfonts}
\usepackage{verbatim} 
\usepackage{float} 
\usepackage{hyperref}
\usepackage{scrtime}

\begin{document}
\SweaveOpts{concordance=TRUE}

\title{GAL Buckle 95}
\author{François Pelletier}
\maketitle
\tableofcontents

\section{Chargement des paquets}
<<>>=
setwd("~/git/GAL-Buckle95/")
library(actuar)
library(MASS)
library(xtable)
library(multicore)
library(moments)
library(TTR)
library(FourierStuff)
library(GeneralizedAsymmetricLaplace)
library(GMMStuff)
library(OptionPricingStuff)
library(QuadraticEstimatingEquations)
@

\section{Constantes et données}

<<>>=
#Nombre de décimales affichées
options(digits=6)
#Marge pour intervalles de confiance
alpha.confint <- 0.05 
#Marge pour test d'hypothèses
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}

<<>>=
EppsPulley.test(RETURNS)
@

\section{Données mises à l'échelle}

<<>>=
scaledRETURNS <- as.vector(scale(RETURNS))
@

\section{Première estimation par QEE}

<<>>=
## Point de départ	
pt.depart <- startparamGAL(scaledRETURNS)
## Fonctions pour les moments
meanQEE <- function(param) mGAL(param,1)
varianceQEE <- function(param) cmGAL(param,2)
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)
dsdQEE <- function(param) dmGAL(param,2)
## Estimation gaussienne
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}