82 lines
2 KiB
R
82 lines
2 KiB
R
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##
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## maximum de vraisemblance avec Vasicek
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##
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library("xtable")
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## importation des données
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data <- read.csv("usgg.csv",header=TRUE, sep=";")[(1:50)*30,]
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delta <- 1/12
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rf <- data$usgg3m/100
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rf[which(rf<=0)] <- 0.001
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##
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## graphique quantile quantile
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##
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pdf("MLE-qqplot-norm.pdf")
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qqnorm(diff(rf))
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qqline
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dev.off()
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## fonction objectif de log-vraisemblance négatif
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VASICEK.FUNOBJ <- function(PAR,RF,DELTA)
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{
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mu <- PAR[2]
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alpha <- PAR[1]
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sigma <- PAR[3]
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n <- length(RF)
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moyenne <- RF[-n] * exp(-alpha*delta)+mu*(1-exp(-alpha*delta))
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variance <- sigma^2 * (1-exp(-2*alpha*delta)) / (2*alpha)
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-sum(dnorm(RF[-1],moyenne,sqrt(variance),log=TRUE))
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}
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ES1 <- optim(c(.5,-.5,.5),fn=VASICEK.FUNOBJ,RF=rf,DELTA=delta)
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##
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## maximum de vraisemblance avec CIR (quasi-vraisemblance normale)
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##
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CIR.QV.FUNOBJ <- function(PAR,RF,DELTA)
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{
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mu <- PAR[2]
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alpha <- PAR[1]
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sigma <- PAR[3]
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n <- length(RF)
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moyenne <- RF[-n] * exp(-alpha * DELTA) +
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mu * (1-exp(-alpha * DELTA))
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variance <- RF[-n] * sigma^2/alpha * (exp(-alpha * DELTA) - exp(-2*alpha * DELTA)) +
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mu * sigma^2/2/alpha*(1-exp(-alpha * DELTA))^2
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-sum(dnorm(RF[-1],moyenne,sqrt(variance),log=TRUE))
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}
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ES3 <- optim(c(alpha.st,mu.st,sigma.st),fn=CIR.QV.FUNOBJ,RF=rf,DELTA=delta)
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##
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## sorties
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##
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ES1$par[3] <- ES1$par[3]^2
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ES3$par[3] <- ES3$par[3]^2
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sink("MLE-dates.tex",append=FALSE,split=FALSE)
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as.vector(data$date[c(1,length(data$date))])
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sink()
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sink("MLE-param.tex",append=FALSE,split=FALSE)
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xtable(cbind(Param=c("alpha","mu","sigma"),
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Vasicek=ES1$par,CIR.QL=ES3$par),
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caption="Paramètres estimés par maximum de vraisemblance pour 2 modèles",
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label="tab:estimParam")
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sink()
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ES1$par
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ES3$par
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##
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## test de ratio de vraisemblance
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##
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loglik <- c(ES1$value,ES3$value)
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n <- length(rf)-1
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1-pchisq(-2*n*(loglik[2]-loglik[1]),4)
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