CPoint: Volatility structural change point estimator

Description

Volatility structural change point estimator

Usage

CPoint(yuima, param1, param2, print=FALSE, symmetrized=FALSE, plot=FALSE)
qmleL(yuima, t,  ...)
qmleR(yuima, t,  ...)

Arguments

yuima

a yuima object.

param1

parameter values before the change point t

param2

parameter values after the change point t

plot

plot test statistics? Default is FALSE.

print some debug output. Default is FALSE.

time value. See Details.

symmetrized

if TRUE uses the symmetrized version of the quasi maximum-likelihood approximation.

...

passed to qmle method. See Examples.

Value

Details

CPoint estimates the change point using quasi-maximum likelihood approach. Function qmleL estimates the parameters in the diffusion matrix using observations up to time t. Function qmleR estimates the parameters in the diffusion matrix using observations from time t to the end. Arguments in both qmleL and qmleR follow the same rules as in qmle.

Examples

Run this code

## Not run: 
# diff.matrix <- matrix(c("theta1.1*x1","0*x2","0*x1","theta1.2*x2"), 2, 2)
# 
# drift.c <- c("1-x1", "3-x2")
# drift.matrix <- matrix(drift.c, 2, 1)
# 
# ymodel <- setModel(drift=drift.matrix, diffusion=diff.matrix, time.variable="t",
# state.variable=c("x1", "x2"), solve.variable=c("x1", "x2"))
# n <- 1000
# 
# set.seed(123)
# 
# t1 <- list(theta1.1=.1, theta1.2=0.2)
# t2 <- list(theta1.1=.6, theta1.2=.6)
# 
# tau <- 0.4
# ysamp1 <- setSampling(n=tau*n, Initial=0, delta=0.01)
# yuima1 <- setYuima(model=ymodel, sampling=ysamp1)
# yuima1 <- simulate(yuima1, xinit=c(1, 1), true.parameter=t1)
# 
# x1 <- yuima1@data@zoo.data[[1]]
# x1 <- as.numeric(x1[length(x1)])
# x2 <- yuima1@data@zoo.data[[2]]
# x2 <- as.numeric(x2[length(x2)])
# 
# ysamp2 <- setSampling(Initial=n*tau*0.01, n=n*(1-tau), delta=0.01)
# yuima2 <- setYuima(model=ymodel, sampling=ysamp2)
# 
# yuima2 <- simulate(yuima2, xinit=c(x1, x2), true.parameter=t2)
# 
# 
# yuima <- yuima1
# yuima@data@zoo.data[[1]] <- c(yuima1@data@zoo.data[[1]], yuima2@data@zoo.data[[1]][-1])
# yuima@data@zoo.data[[2]] <- c(yuima1@data@zoo.data[[2]], yuima2@data@zoo.data[[2]][-1])
# 
# plot(yuima)
# 
# # estimation of change point for given parameter values
# t.est <- CPoint(yuima,param1=t1,param2=t2, plot=TRUE)
# 
# 
# low <- list(theta1.1=0, theta1.2=0)
# 
# # first state estimate of parameters using small 
# # portion of data in the tails
# tmp1 <- qmleL(yuima,start=list(theta1.1=0.3,theta1.2=0.5),t=1.5,
#         lower=low, method="L-BFGS-B")
# tmp1
# tmp2 <- qmleR(yuima,start=list(theta1.1=0.3,theta1.2=0.5), t=8.5,
#         lower=low, method="L-BFGS-B")
# tmp2
# 
# 
# # first stage changepoint estimator
# t.est2 <- CPoint(yuima,param1=coef(tmp1),param2=coef(tmp2))
# t.est2$tau
# 
# 
# # second stage estimation of parameters given first stage
# # change point estimator
# tmp11 <- qmleL(yuima,start=as.list(coef(tmp1)), t=t.est2$tau-0.1,
#  lower=low, method="L-BFGS-B")
# tmp11
# 
# tmp21 <- qmleR(yuima,start=as.list(coef(tmp2)), t=t.est2$tau+0.1,
#  lower=low, method="L-BFGS-B")
# tmp21
# 
# # second stage estimator of the change point
# CPoint(yuima,param1=coef(tmp11),param2=coef(tmp21))
# 
# 
# ## One dimensional example: non linear case
# diff.matrix <- matrix("(1+x1^2)^theta1", 1, 1)
# drift.c <- c("x1")
# 
# ymodel <- setModel(drift=drift.c, diffusion=diff.matrix, time.variable="t",
# state.variable=c("x1"), solve.variable=c("x1"))
# n <- 500
# 
# set.seed(123)
# 
# y0 <- 5 # initial value
# theta00 <- 1/5
# gamma <- 1/4
# 
# 
# theta01 <- theta00+n^(-gamma)
# 
# 
# t1 <- list(theta1= theta00)
# t2 <- list(theta1= theta01)
# 
# tau <- 0.4
# ysamp1 <- setSampling(n=tau*n, Initial=0, delta=1/n)
# yuima1 <- setYuima(model=ymodel, sampling=ysamp1)
# yuima1 <- simulate(yuima1, xinit=c(5), true.parameter=t1)
# x1 <- yuima1@data@zoo.data[[1]]
# x1 <- as.numeric(x1[length(x1)])
# 
# ysamp2 <- setSampling(Initial=tau, n=n*(1-tau), delta=1/n)
# yuima2 <- setYuima(model=ymodel, sampling=ysamp2)
# 
# yuima2 <- simulate(yuima2, xinit=c(x1), true.parameter=t2)
# 
# 
# yuima <- yuima1
# yuima@data@zoo.data[[1]] <- c(yuima1@data@zoo.data[[1]], yuima2@data@zoo.data[[1]][-1])
# 
# 
# plot(yuima)
# 
# 
# t.est <- CPoint(yuima,param1=t1,param2=t2)
# t.est$tau
# 
# low <- list(theta1=0)
# upp <- list(theta1=1)
# 
# # first state estimate of parameters using small 
# # portion of data in the tails
# tmp1 <- qmleL(yuima,start=list(theta1=0.5),t=.15,lower=low, upper=upp,method="L-BFGS-B")
# tmp1
# tmp2 <- qmleR(yuima,start=list(theta1=0.5), t=.85,lower=low, upper=upp,method="L-BFGS-B")
# tmp2
# 
# 
# 
# # first stage changepoint estimator
# t.est2 <- CPoint(yuima,param1=coef(tmp1),param2=coef(tmp2))
# t.est2$tau
# 
# 
# # second stage estimation of parameters given first stage
# # change point estimator
# tmp11 <- qmleL(yuima,start=as.list(coef(tmp1)), t=t.est2$tau-0.1,
#    lower=low, upper=upp,method="L-BFGS-B")
# tmp11
# 
# tmp21 <- qmleR(yuima,start=as.list(coef(tmp2)), t=t.est2$tau+0.1,
#   lower=low, upper=upp,method="L-BFGS-B")
# tmp21
# 
# 
# # second stage estimator of the change point
# CPoint(yuima,param1=coef(tmp11),param2=coef(tmp21),plot=TRUE)
# ## End(Not run)

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