EULERloglik | R Documentation |
Euler approximation of the likelihood of a process solution of a stochastic differential equation. These functions are useful to calculate approximated maximum likelihood estimators when the transition density of the process is not known.
EULERloglik(X, theta, d, s, log = TRUE)
X |
a ts object containing a sample path of an sde. |
theta |
vector of parameters. |
d,s |
drift and diffusion coefficients; see details. |
log |
logical; if TRUE, the log-likelihood is returned. |
The function EULERloglik
returns the Euler approximation of the
log-likelihood. The functions s
and d
are the drift and diffusion
coefficients with arguments (t,x,theta)
.
x |
a number |
Stefano Maria Iacus
set.seed(123) d <- expression(-1*x) s <- expression(2) sde.sim(drift=d, sigma=s) -> 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(-3,3,length=100) sapply(xx, function(x) true.loglik(c(x,4))) -> py sapply(xx, function(x) EULERloglik(X,c(x,4),B,S)) -> pz # true likelihood plot(xx,py,type="l",xlab=expression(beta),ylab="log-likelihood") lines(xx,pz, lty=2) # Euler
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