R Under development (unstable) (2024-03-03 r86036 ucrt) -- "Unsuffered Consequences"
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> library(Sim.DiffProc)
Package 'Sim.DiffProc', version 4.9
browseVignettes('Sim.DiffProc') for more informations.
> 
> 
> ## 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)
Pseudo maximum likelihood estimation

Method:  Euler
Call:
function (name, ...)  .Primitive("call")

Coefficients:
         Estimate Std. Error
theta1  2.0769516 0.98838467
theta2 -0.2631871 0.19544290
theta3  0.1302158 0.02523105
theta4  1.4513173 0.10323740

-2 log L: 475.7572 
> summary(fitmod2)
Pseudo maximum likelihood estimation

Method:  Euler
Call:
function (name, ...)  .Primitive("call")

Coefficients:
         Estimate Std. Error
theta1  2.6387593 1.18754723
theta2 -0.3606083 0.18896205
theta3  0.8650745 0.03549428

-2 log L: 563.7025 
> coef(fitmod1)
    theta1     theta2     theta3     theta4 
 2.0769516 -0.2631871  0.1302158  1.4513173 
> coef(fitmod2)
    theta1     theta2     theta3 
 2.6387593 -0.3606083  0.8650745 
> confint(fitmod1,parm=c('theta2','theta3'))
             2.5 %    97.5 %
theta2 -0.64624812 0.1198740
theta3  0.08076388 0.1796678
> confint(fitmod2,parm=c('theta2','theta3'))
            2.5 %      97.5 %
theta2 -0.7309671 0.009750471
theta3  0.7955070 0.934642013
> AIC(fitmod1)
[1] 483.7572
> AIC(fitmod2)
[1] 569.7025
> 
> proc.time()
   user  system elapsed 
   0.35    0.09    0.43