| cpoint {sde} | R Documentation |
Volatility change point estimator for diffusion processes based on leasts squares
cpoint(x, mu, sigma)
x |
a ts object. |
mu |
a function of x describing the drift coefficient. |
sigma |
a function of x describing the diffusion coefficient. |
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 following 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 following model is considered
dXt = b(Xt)dt + theta*dWt
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)