cpoint | R Documentation |
Volatility change-point estimator for diffusion processes based on least squares.
cpoint(x, mu, sigma)
x |
a |
mu |
a function of |
sigma |
a function of |
The function returns a list of elements containing the discrete k0
and continuous tau0
change-point instant, the estimated volatilities before (theta1
) and after (theta2
) the time change.
The model is assumed to be of the form
dXt = b(Xt)dt + theta*sigma(Xt)dWt
where theta
= theta1
for t<=tau0
and theta
= theta2
otherwise.
If the drift coefficient is unknown, the model
dXt = b(Xt)dt + θ*dWt
is considered and b
is estimated nonparametrically.
X |
a list |
Stefano Maria Iacus
tau0 <- 0.6 k0 <- ceiling(1000*tau0) set.seed(123) X1 <- sde.sim(X0=1, N=2*k0, t0=0, T=tau0, model="CIR", theta=c(6,2,1)) X2 <- sde.sim(X0=X1[2*k0+1], N=2*(1000-k0), t0=tau0, T=1, model="CIR", theta=c(6,2,3)) Y <- ts(c(X1,X2[-1]), start=0, deltat=deltat(X1)) X <- window(Y,deltat=0.01) DELTA <- deltat(X) n <- length(X) mu <- function(x) 6-2*x sigma <- function(x) sqrt(x) cp <- cpoint(X,mu,sigma) cp plot(X) abline(v=tau0,lty=3) abline(v=cp$tau0,col="red") # nonparametric estimation cpoint(X)
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