qmleLevy | R Documentation |
Calculate the Gaussian quasi-likelihood and Gaussian quasi-likelihood estimators of Levy driven SDE.
qmleLevy(yuima, start, lower, upper, joint = FALSE, third = FALSE, Est.Incr = "NoIncr", aggregation = TRUE)
yuima |
a yuima object. |
lower |
a named list for specifying lower bounds of parameters. |
upper |
a named list for specifying upper bounds of parameters. |
start |
initial values to be passed to the optimizer. |
joint |
perform joint estimation or two stage estimation, by default |
third |
perform third estimation by default |
Est.Incr |
the qmleLevy returns an object of |
aggregation |
If |
This function performs Gaussian quasi-likelihood estimation for Levy driven SDE.
first |
estimated values of first estimation (scale parameters) |
second |
estimated values of second estimation (drift parameters) |
third |
estimated values of third estimation (scale parameters) |
The function qmleLevy
uses the function qmle
internally.
It can be applied only for the standardized Levy noise whose moments of any order exist.
In present yuima
package, birateral gamma (bgamma) process, normal inverse Gaussian (NIG) process, variance gamma (VG) process, and normal tempered stable process are such candidates.
In the current version, the standardization condition on the driving noise is internally checked only for the one-dimensional noise.
The standardization condition for the multivariate noise is given in
or
They also contain more presice explanation of this function.
The YUIMA Project Team
Contacts: Yuma Uehara y-uehara@ism.ac.jp
Masuda, H. (2013). Convergence of Gaussian quasi-likelihood random fields for ergodic Levy driven SDE observed at high frequency. The Annals of Statistics, 41(3), 1593-1641.
Masuda, H. and Uehara, Y. (2017). On stepwise estimation of Levy driven stochastic differential equation (Japanese) ., Proc. Inst. Statist. Math., accepted.
## Not run: ## One-dimensional case dri<-"-theta0*x" ## set drift jum<-"theta1/(1+x^2)^(-1/2)" ## set jump yuima<-setModel(drift = dri ,jump.coeff = jum ,solve.variable = "x",state.variable = "x" ,measure.type = "code" ,measure = list(df="rbgamma(z,1,sqrt(2),1,sqrt(2))")) ## set true model n<-3000 T<-30 ## terminal hn<-T/n ## stepsize sam<-setSampling(Terminal = T, n=n) ## set sampling scheme yuima<-setYuima(model = yuima, sampling = sam) ## model true<-list(theta0 = 1,theta1 = 2) ## true values upper<-list(theta0 = 4, theta1 = 4) ## set upper bound lower<-list(theta0 = 0.5, theta1 = 1) ## set lower bound set.seed(123) yuima<-simulate(yuima, xinit = 0, true.parameter = true,sampling = sam) ## generate a path start<-list(theta0 = runif(1,0.5,4), theta1 = runif(1,1,4)) ## set initial values qmleLevy(yuima,start=start,lower=lower,upper=upper, joint = TRUE) ## Multi-dimensional case lambda<-1/2 alpha<-1 beta<-c(0,0) mu<-c(0,0) Lambda<-matrix(c(1,0,0,1),2,2) ## set parameters in noise dri<-c("1-theta0*x1-x2","-theta1*x2") jum<-matrix(c("x1*theta2+1","0","0","1"),2,2) ## set coefficients yuima <- setModel(drift=dri, solve.variable=c("x1","x2"),state.variable = c("x1","x2"), jump.coeff=jum, measure.type="code", measure=list(df="rvgamma(z, lambda, alpha, beta, mu, Lambda )")) n<-3000 ## the number of total samples T<-30 ## terminal hn<-T/n ## stepsize sam<-setSampling(Terminal = T, n=n) ## set sampling scheme yuima<-setYuima(model = yuima, sampling = sam) ## model true<-list(theta0 = 1,theta1 = 2,theta2 = 3,lambda=lambda, alpha=alpha, beta=beta,mu=mu, Lambda=Lambda) ## true values upper<-list(theta0 = 4, theta1 = 4, theta2 = 5, lambda=lambda, alpha=alpha, beta=beta,mu=mu, Lambda=Lambda) ## set upper bound lower<-list(theta0 = 0.5, theta1 = 1, theta2 = 1, lambda=lambda, alpha=alpha, beta=beta,mu=mu, Lambda=Lambda) ## set lower bound set.seed(123) yuima<-simulate(yuima, xinit = c(0,0), true.parameter = true,sampling = sam) ## generate a path plot(yuima) start<-list(theta0 = runif(1,0.5,4), theta1 = runif(1,1,4), theta2 = runif(1,1,5),lambda=lambda, alpha=alpha, beta=beta,mu=mu, Lambda=Lambda) ## set initial values qmleLevy(yuima,start=start,lower=lower,upper=upper,joint = FALSE,third=TRUE) ## End(Not run)
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