permfn1 {extremogram}

Confidence bands for the sample univariate extremogram

Description

The function estimates empirical confidence bands for the sample univariate extremogram via a permutation procedure under the assumption that the data are independent.

Usage

permfn1(x, p, m, type, exttype, maxlag, start = 1, alpha = 0.05)

Arguments

x

Univariate time series (a vector).

p

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

m

Number of permutations (an integer).

type

Type of confidence bands. If type=1, it adds all permutations to the sample extremogram plot. If type=2, it adds the alpha/2 and (1-alpha)/2 empirical confidence bands for each lag. If type=3, it calculates the lag 1 alpha/2 and (1-alpha)/2 empirical confidence bands lag and uses them for all of the lags.

exttype

Extremogram type (see extremogram1).

maxlag

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

start

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

alpha

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

Value

The empirical confidence bands are added to the sample univariate extremogram plot.

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
alpha   = 0.1
beta    = 0.6
n       = 1000
quant   = 0.95
exttype = 1
maxlag  = 70
df      = 3
type    = 3
m       = 10
G = extremogram:::garchsim(omega,alpha,beta,n,df)

extremogram1(G, quant, maxlag, exttype, 1, 1, 0)
permfn1(G, quant, m, type, exttype, maxlag, 1, 0.05)