library(Sim.DiffProc)


## Application to real data
## CKLS modele vs CIR modele 
## CKLS (mod1):  dX(t) = (theta1+theta2* X(t))* dt + theta3 * X(t)^theta4 * dW(t)
## CIR  (mod2):  dX(t) = (theta1+theta2* X(t))* dt + theta3 * sqrt(X(t))  * dW(t)
set.seed(1234)

data(Irates)
rates <- Irates[,"r1"]
rates <- window(rates, start=1964.471, end=1989.333)

fx1 <- expression(theta[1]+theta[2]*x)
gx1 <- expression(theta[3]*x^theta[4])
gx2 <- expression(theta[3]*sqrt(x))

fitmod1 <- fitsde(rates,drift=fx1,diffusion=gx1,pmle="euler",start = list(theta1=1,theta2=1,
                  theta3=1,theta4=1),optim.method = "L-BFGS-B")
fitmod2 <- fitsde(rates,drift=fx1,diffusion=gx2,pmle="euler",start = list(theta1=1,theta2=1,
                  theta3=1),optim.method = "L-BFGS-B")	
summary(fitmod1)
summary(fitmod2)
coef(fitmod1)
coef(fitmod2)
confint(fitmod1,parm=c('theta2','theta3'))
confint(fitmod2,parm=c('theta2','theta3'))
AIC(fitmod1)
AIC(fitmod2)