R: Wild Bootstrap Test for the Absence of Lead-Lag Effects

llag.test {yuima}

R Documentation

Wild Bootstrap Test for the Absence of Lead-Lag Effects

Description

Tests the absence of lead-lag effects (time-lagged correlations) by the wild bootstrap procedure proposed in Koike (2017) for each pair of components.

Usage

llag.test(x, from = -Inf, to = Inf, division = FALSE, grid, R = 999,
          parallel = "no", ncpus = getOption("boot.ncpus", 1L),
          cl = NULL, tol = 1e-06)

Arguments

`x`	an object of `yuima-class` or `yuima.data-class`.
`from`	a numeric vector each of whose component(s) indicates the lower end of a finite grid on which the contrast function is evaluated, if `grid` is missing.
`to`	a numeric vector each of whose component(s) indicates the upper end of a finite grid on which the contrast function is evaluated, if `grid` is missing.
`division`	a numeric vector each of whose component(s) indicates the number of the points of a finite grid on which the contrast function is evaluated, if `grid` is missing.
`grid`	a numeric vector or a list of numeric vectors. See 'Details' of `llag`.
`R`	a single positive integer indicating the number of bootstrap replicates.
`parallel`	passed to `boot`.
`ncpus`	passed to `boot`.
`cl`	passed to `boot`.
`tol`	tolelance parameter to avoid numerical errors in comparison of time stamps. All time stamps are divided by `tol` and rounded to integers. Note that the values of `grid` are also divided by `tol` and rounded to integers. A reasonable choice of `tol` is the minimum unit of time stamps. The default value `1e-6` supposes that the minimum unit of time stamps is greater or equal to 1 micro-second.

Details

For each pair of components, this function performs the wild bootstrap procedure proposed in Koike (2017) to test whether there is a (possibly) time-lagged correlation. The null hypothesis of the test is that there is no time-lagged correlation and the alternative is its negative. The test regects the null hypothesis if the maximum of the absolute values of cross-covariances is too large. The critical region is constructed by a wild bootstrap procedure with Rademacher variables as the multiplier variables.

Value

`p.values`	a matrix whose components indicate the bootstrap p-values for the corresponding pair of components.
`max.cov`	a matrix whose componenets indicate the maxima of the absolute values of cross-covariances for the corresponding pair of components.
`max.corr`	a matrix whose componenets indicate the maxima of the absolute values of cross-correlations for the corresponding pair of components.

Author(s)

Yuta Koike with YUIMA Project Team

References

Koike, Y. (2019). Gaussian approximation of maxima of Wiener functionals and its application to high-frequency data, Annals of Statistics, 47, 1663–1687. doi:10.1214/18-AOS1731.

Examples

## Not run: 
# The following example is taken from mllag

## Set a model
diff.coef.matrix <- matrix(c("sqrt(x1)", "3/5*sqrt(x2)",
 "1/3*sqrt(x3)", "", "4/5*sqrt(x2)","2/3*sqrt(x3)",
 "","","2/3*sqrt(x3)"), 3, 3) 
drift <- c("1-x1","2*(10-x2)","3*(4-x3)")
cor.mod <- setModel(drift = drift, 
 diffusion = diff.coef.matrix,
 solve.variable = c("x1", "x2","x3")) 

set.seed(111) 

## We use a function poisson.random.sampling 
## to get observation by Poisson sampling.
yuima.samp <- setSampling(Terminal = 1, n = 1200) 
yuima <- setYuima(model = cor.mod, sampling = yuima.samp) 
yuima <- simulate(yuima,xinit=c(1,7,5)) 

## intentionally displace the second time series

  data2 <- yuima@data@zoo.data[[2]]
  time2 <- time(data2)
  theta2 <- 0.05   # the lag of x2 behind x1
  stime2 <- time2 + theta2  
  time(yuima@data@zoo.data[[2]]) <- stime2

  data3 <- yuima@data@zoo.data[[3]]
  time3 <- time(data3)
  theta3 <- 0.12   # the lag of x3 behind x1
  stime3 <- time3 + theta3 
  time(yuima@data@zoo.data[[3]]) <- stime3

## sampled data by Poisson rules
psample<- poisson.random.sampling(yuima, 
 rate = c(0.2,0.3,0.4), n = 1000) 
 
 ## We search lead-lag parameters on the interval [-0.1, 0.1] with step size 0.01 
G <- seq(-0.1,0.1,by=0.01)

## perform lead-lag test
llag.test(psample, grid = G, R = 999)

## Since the lead-lag parameter for the pair(x1, x3) is not contained in G,
## the null hypothesis is not rejected for this pair

## End(Not run)

[Package yuima version 1.15.27 Index]