bns.test {yuima}

Barndorff-Nielsen and Shephard's Test for the Presence of Jumps Using Bipower Variation

Description

Tests the presence of jumps using the statistic proposed in Barndorff-Nielsen and Shephard (2004,2006) for each component.

Usage

bns.test(yuima, r = rep(1, 4), type = "standard", adj = TRUE)

Arguments

yuima

an object of yuima-class or yuima.data-class.

r

a vector of non-negative numbers or a list of vectors of non-negative numbers. Theoretically, it is necessary that sum(r)=4 and max(r)<2.

type

type of the test statistic to use. standard is default.

adj

logical; if TRUE, the maximum adjustment suggested in Barndorff-Nielsen and Shephard (2004) is applied to the test statistic when type is equal to either “log” or “ratio”.

Details

For the i-th component, the test statistic is equal to the i-th component of sqrt(n)*(mpv(yuima,2)-mpv(yuima,c(1,1)))/sqrt(vartheta*mpv(yuima,r)) when type="standard", sqrt(n)*log(mpv(yuima,2)/mpv(yuima,c(1,1)))/sqrt(vartheta*mpv(yuima,r)/mpv(yuima,c(1,1))^2) when type="log" and sqrt(n)*(1-mpv(yuima,c(1,1))/mpv(yuima,2))/sqrt(vartheta*mpv(yuima,r)/mpv(yuima,c(1,1))^2) when type="ratio". Here, n is equal to the length of the i-th component of the zoo.data of yuima minus 1 and vartheta is pi^2/4+pi-5. When adj=TRUE, mpv(yuima,r)[i]/mpv(yuima,c(1,1))^2)[i] is replaced with 1 if it is less than 1.

Value

A list with the same length as the zoo.data of yuima. Each component of the list has class “htest” and contains the following components:

statistic

the value of the test statistic of the corresponding component of the zoo.data of yuima.

p.value

an approximate p-value for the test of the corresponding component.

method

the character string “Barndorff-Nielsen and Shephard jump test”.

data.name

the character string “xi”, where i is the number of the component.

Note

Theoretically, this test may be invalid if sampling is irregular.

Author(s)

Yuta Koike with YUIMA Project Team

References

Barndorff-Nielsen, O. E. and Shephard, N. (2004) Power and bipower variation with stochastic volatility and jumps, Journal of Financial Econometrics, 2, no. 1, 1–37.

Barndorff-Nielsen, O. E. and Shephard, N. (2006) Econometrics of testing for jumps in financial economics using bipower variation, Journal of Financial Econometrics, 4, no. 1, 1–30.

Huang, X. and Tauchen, G. (2005) The relative contribution of jumps to total price variance, Journal of Financial Econometrics, 3, no. 4, 456–499.

See Also

lm.jumptest, mpv, minrv.test, medrv.test, pz.test

Examples

set.seed(123)

# One-dimensional case
## Model: dXt=t*dWt+t*dzt, 
## where zt is a compound Poisson process with intensity 5 and jump sizes distribution N(0,0.1).

model <- setModel(drift=0,diffusion="t",jump.coeff="t",measure.type="CP",
                  measure=list(intensity=5,df=list("dnorm(z,0,sqrt(0.1))")),
                  time.variable="t")

yuima.samp <- setSampling(Terminal = 1, n = 390) 
yuima <- setYuima(model = model, sampling = yuima.samp) 
yuima <- simulate(yuima)
plot(yuima) # The path seems to involve some jumps

bns.test(yuima) # standard type

bns.test(yuima,type="log") # log type

bns.test(yuima,type="ratio") # ratio type

# Multi-dimensional case
## Model: dXkt=t*dWk_t (k=1,2,3) (no jump case).

diff.matrix <- diag(3)
diag(diff.matrix) <- c("t","t","t")
model <- setModel(drift=c(0,0,0),diffusion=diff.matrix,time.variable="t",
                  solve.variable=c("x1","x2","x3"))

yuima.samp <- setSampling(Terminal = 1, n = 390) 
yuima <- setYuima(model = model, sampling = yuima.samp) 
yuima <- simulate(yuima)
plot(yuima)

bns.test(yuima)