Nothing
require(sde)
# ex3.08.R
set.seed(123)
d <- expression(-1*x)
s <- expression(2)
sde.sim(drift=d, sigma=s,N=50,delta=0.01) -> X
S <- function(t, x, theta) sqrt(theta[2])
B <- function(t, x, theta) -theta[1]*x
true.loglik <- function(theta) {
DELTA <- deltat(X)
lik <- 0
for(i in 2:length(X))
lik <- lik + dnorm(X[i], mean=X[i-1]*exp(-theta[1]*DELTA),
sd = sqrt((1-exp(-2*theta[1]*DELTA))*theta[2]/(2*theta[1])),TRUE)
lik
}
xx <- seq(-10,10,length=20)
sapply(xx, function(x) true.loglik(c(x,4))) -> py
sapply(xx, function(x) EULERloglik(X,c(x,4),B,S)) -> pz
sapply(xx, function(x) SIMloglik(X,c(x,4),B,S,M=10000,N=5)) -> pw
par(mar=c(5,5,1,1))
plot(xx,py, type="l", xlab=expression(beta), ylab="log-likelihood")
lines(xx, pz, lty=2)
lines(xx, pw, lty=3)
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