extremogram2 {extremogram}

Sample cross extremogram

Description

The function estimates the sample cross extremogram and creates an extremogram plot.

Usage

extremogram2(a, quant1, quant2, maxlag, type, ploting = 1, cutoff = 1,
  start = 0)

Arguments

a

Bivariate time series (n by 2 matrix).

quant1

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

quant2

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

maxlag

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

type

If type=1, the upper tail extremogram is estimated - P(Y>y,X>x). If type=2, the lower tail extremogram is estimated - P(Y<y,X<x). If type=3, the extremogram is estimated for a lower tail extreme value in the first time series and an upper tail extreme value in the second time series - P(Y>y,X<x). If type=4, the extremogram is estimated for a lower tail extreme value in the second time series and an upper tail extreme value in the first time series - P(Y<y,X>x).

ploting

An extremogram plot. If ploting = 1, a plot is created (default). If ploting = 0, no plot is created.

cutoff

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

start

The lag that the extremogram plots starts at (an integer not greater than maxlag, default is 0).

Value

Cross extremogram values and a plot (if requested).

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
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)