bootconf2 {extremogram}

Confidence bands for the sample cross extremogram

Description

The function estimates confidence bands for the sample cross extremogram using the stationary bootstrap.

Usage

bootconf2(x, R, l, maxlag, quant1, quant2, type, par, start = 1, cutoff = 1,
  alpha = 0.05)

Arguments

x

Bivariate time series (n by 2 matrix).

R

Number of bootstrap replications (an integer).

l

Mean block size for stationary bootstrap or mean of the geometric distribution used to generate resampling blocks (an integer that is not longer than the length of the time series).

maxlag

Number of lags to include in the extremogram (an integer).

quant1

Quantile of the first time series to indicate an extreme event (a number between 0 and 1).

quant2

Quantile of the second series to indicate an extreme event (a number between 0 and 1).

type

Extremogram type (see function extremogram2).

par

If par = 1, the bootstrap replication procedure will be parallelized. If par = 0, no parallelization will be used.

start

The lag that the extremogram plots starts at (an integer not greater than maxlag, default is 1).

cutoff

The cutoff of the y-axis on the plot (a number between 0 and 1, default is 1).

alpha

Significance level for the confidence bands (a number between 0 and 1, default is 0.05).

Value

Returns a plot of the confidence bands for the sample cross extremogram.

References

1. Davis, R. A., Mikosch, T., & Cribben, I. (2012). Towards estimating extremal serial dependence via the bootstrapped extremogram. Journal of Econometrics,170(1), 142-152.

2. Davis, R. A., Mikosch, T., & Cribben, I. (2011). Estimating extremal dependence in univariate and multivariate time series via the extremogram.arXiv preprint arXiv:1107.5592.

Examples

# generate a GARCH(1,1) process
omega  = 1
alpha1 = 0.1
beta1  = 0.6
alpha2 = 0.11
beta2  = 0.78
n      = 1000
quant  = 0.95
type   = 1
maxlag = 70
df     = 3
R      = 10
l      = 30
par    = 0
G1     = extremogram:::garchsim(omega,alpha1,beta1,n,df)
G2     = extremogram:::garchsim(omega,alpha2,beta2,n,df)
data   = cbind(G1, G2)

extremogram2(data, quant, quant, maxlag, type, 1, 1, 0)
bootconf2(data, R, l, maxlag, quant, quant, type, par, 1, 1, 0.05)