cpoint {sde}R Documentation

Volatility change point estimator for diffusion processes

Description

Volatility change point estimator for diffusion processes based on leasts squares

Usage

cpoint(x, mu, sigma)

Arguments

x a ts object.
mu a function of x describing the drift coefficient.
sigma a function of x describing the diffusion coefficient.

Details

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.

Value

X a list

Author(s)

Stefano Maria Iacus

Examples

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)

[Package sde version 1.9.33 Index]