lm.jumptest {yuima}

Lee and Mykland's Test for the Presence of Jumps Using Normalized Returns

Description

Performs a test for the null hypothesis that the realized path has no jump following Lee and Mykland (2008).

Usage

lm.jumptest(yuima, K)

Arguments

yuima

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

K

a positive integer indicating the window size to compute local variance estimates. It can be specified as a vector to use different window sizes for different components. The default value is K=pmin(floor(sqrt(252*n)), n) with n=length(yuima)-1, following Lee and Mykland (2008) as well as Dumitru and Urga (2012).

Value

A list with the same length as dim(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 yuima.

p.value

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

method

the character string “Lee and Mykland jump test”.

data.name

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

Author(s)

Yuta Koike with YUIMA Project Team

References

Dumitru, A.-M. and Urga, G. (2012) Identifying jumps in financial assets: A comparison between nonparametric jump tests. Journal of Business and Economic Statistics, 30, 242–255.

Lee, S. S. and Mykland, P. A. (2008) Jumps in financial markets: A new nonparametric test and jump dynamics. Review of Financial Studies, 21, 2535–2563.

Maneesoonthorn, W., Martin, G. M. and Forbes, C. S. (2020) High-frequency jump tests: Which test should we use? Journal of Econometrics, 219, 478–487.

Theodosiou, M. and Zikes, F. (2011) A comprehensive comparison of alternative tests for jumps in asset prices. Central Bank of Cyprus Working Paper 2011-2.

See Also

bns.test, 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(0,1).

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

lm.jumptest(yuima) # p-value is very small, so the path would have a jump
lm.jumptest(yuima, K = floor(sqrt(390))) # different value of K

# Multi-dimensional case
## Model: Bivariate standard BM + CP
## Only the first component has jumps

mod <- setModel(drift = c(0, 0), diffusion = diag(2),
                jump.coeff = diag(c(1, 0)),
                measure = list(intensity = 5, 
                               df = "dmvnorm(z,c(0,0),diag(2))"),
                jump.variable = c("z"), measure.type=c("CP"),
                solve.variable=c("x1","x2"))

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

lm.jumptest(yuima) # test is performed component-wise