JBtest function

Remove Jumps and Calculate the Gaussian Quasi-likelihood Estimator Based on the Jarque-Bera Normality Test

Remove jumps and calculate the Gaussian quasi-likelihood estimator based on the Jarque-Bera normality test UTF-8

JBtest(yuima,start,lower,upper,alpha,skewness=TRUE,kurtosis=TRUE,withdrift=FALSE)

Arguments

• yuima: a yuima object (diffusion with compound Poisson jumps).
• lower: a named list for specifying lower bounds of parameters.
• upper: a named list for specifying upper bounds of parameters.
• alpha: significance level of Jarque-Bera normality test.
• start: initial values to be passed to the optimizer.
• skewness: use third moment information ? by default, skewness=TRUE
• kurtosis: use fourth moment information ? by default, kurtosis=TRUE
• withdrift: use drift information for constructing self-normalized residuals or not? by default, withdrift = FALSE

Details

This function removes large increments which are regarded as jumps based on the iterative Jarque-Bera normality test, and after that, calculates the Gaussian quasi maximum likelihood estimator.

Returns

• Removed: Removed jumps and jump times

• OGQMLE: Gaussian quasi maximum likelihood estimator before jump removal

• JRGQMLE: Gaussian quasi maximum likelihood estimator after jump removal

• Figures: For visualization, the jump points are presented. In addition, the histogram of the jump removed self-normalized residuals, transition of the estimators and the logarithm of Jarque-Bera statistics are given as figures

References

Masuda, H. (2013). Asymptotics for functionals of self-normalized residuals of discretely observed stochastic processes. Stochastic Processes and their Applications 123 (2013), 2752--2778.

Masuda, H. and Uehara, Y. (2021). Estimating Diffusion With Compound Poisson Jumps Based On Self-normalized Residuals. Journal of Statistical Planning and Inference., 215, 158--183.

Author(s)

The YUIMA Project Team

Contacts: Yuma Uehara y-uehara@kansai-u.ac.jp

Examples

## Not run:

set.seed(123)
mod <- setModel(drift="10-3*x",
                diffusion="theta*(2+x^2)/(1+x^2)",
               jump.coeff="1",
               measure=list(intensity="1",df=list("dunif(z, 3, 5)")),
               measure.type="CP")

T <- 10 ## Terminal
n <- 5000 ## generation size
samp <- setSampling(Terminal=T, n=n) ## define sampling scheme
yuima <- setYuima(model = mod, sampling = samp)

yuima <- simulate(yuima, xinit=1,true.parameter=list(theta=sqrt(2)), sampling = samp)

JBtest(yuima,start=list(theta=0.5),upper=c(theta=100)
,lower=c(theta=0),alpha=0.01)
## End(Not run)