| Type: | Package |
| Title: | Estimation of Extreme Value Dependence for Time Series Data |
| Version: | 1.0.2 |
| Date: | 2015-09-24 |
| Author: | Nadezda Frolova, Ivor Cribben |
| Maintainer: | Nadezda Frolova <nfrolova@ualberta.ca> |
| Description: | Estimation of the sample univariate, cross and return time extremograms. The package can also adds empirical confidence bands to each of the extremogram plots via a permutation procedure under the assumption that the data are independent. Finally, the stationary bootstrap allows us to construct credible confidence bands for the extremograms. |
| License: | GPL-3 |
| Imports: | boot(≥ 1.3-11), MASS(≥ 7.3-31), parallel(≥ 3.1.1) |
| Depends: | R (≥ 3.1.0) |
| NeedsCompilation: | no |
| Packaged: | 2016-10-07 18:20:58 UTC; Nadia |
| Repository: | CRAN |
| Date/Publication: | 2016-10-08 08:48:07 |
extremogram
Description
The package estimates the sample univariate, cross and return time extremograms. It can also add empirical confidence bands to each of the extremogram plots via a permutation procedure under the assumption that the data are independent. Finally, the stationary bootstrap allows us to construct credible confidence bands for the extremograms.
Functions:
Author(s)
Nadezda Frolova <nfrolova@ualberta.ca>, Ivor Cribben <cribben@ualberta.ca>
References
Davis, R. A., Mikosch, T., & Cribben, I. (2012). Towards estimating extremal serial dependence via the bootstrapped extremogram. Journal of Econometrics,170(1), 142-152.
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.
Confidence bands for the sample univariate extremogram
Description
The function estimates confidence bands for the sample univariate extremogram using the stationary bootstrap.
Usage
bootconf1(x, R, l, maxlag, quant, type, par, start = 1, cutoff = 1,
alpha = 0.05)
Arguments
x |
Univariate time series (a vector). |
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). |
quant |
Quantile of the time series to indicate an extreme event (a number between 0 and 1). |
type |
Extremogram type (see function |
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 |
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 univariate extremogram.
References
Davis, R. A., Mikosch, T., & Cribben, I. (2012). Towards estimating extremal serial dependence via the bootstrapped extremogram. Journal of Econometrics,170(1), 142-152.
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
type = 1
maxlag = 70
df = 3
R = 10
l = 30
par = 0
G = extremogram:::garchsim(omega,alpha,beta,n,df)
extremogram1(G, quant, maxlag, type, 1, 1, 0)
bootconf1(G, R, l, maxlag, quant, type, par, 1, 1, 0.05)
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 |
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 |
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
Davis, R. A., Mikosch, T., & Cribben, I. (2012). Towards estimating extremal serial dependence via the bootstrapped extremogram. Journal of Econometrics,170(1), 142-152.
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)
Confidence bands for the sample return time extremogram
Description
The function estimates confidence bands for the sample return time extremogram using the stationary bootstrap.
Usage
bootconfr(x, R, l, maxlag, uplevel = 1, lowlevel = 0, type, par,
start = 1, cutoff = 1, alpha = 0.05)
Arguments
x |
Univariate time series (a vector). |
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) |
uplevel |
Quantile of the time series to indicate a upper tail extreme event (a number between 0 and 1, default is 1). |
lowlevel |
Quantile of the time series to indicate a lower tail extreme event (a number between 0 and 1, default is 0). |
type |
Extremogram type (see function |
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 |
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 return time extremogram.
References
Davis, R. A., Mikosch, T., & Cribben, I. (2012). Towards estimating extremal serial dependence via the bootstrapped extremogram. Journal of Econometrics,170(1), 142-152.
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
uplevel = 0.95
lowlevel = 0.05
type = 3
maxlag = 70
df = 3
R = 10
l = 30
par = 0
G = extremogram:::garchsim(omega,alpha,beta,n,df)
extremogramr(G, type, maxlag, uplevel, lowlevel, 1, 1)
bootconfr(G, R, l, maxlag, uplevel, lowlevel, type, par, 1, 1, 0.05)
Sample univariate extremogram
Description
The function estimates the sample univariate extremogram and creates an extremogram plot.
Usage
extremogram1(x, quant, maxlag, type, ploting = 1, cutoff = 1, start = 0)
Arguments
x |
Univariate time series (a vector). |
quant |
Quantile of the 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 |
Extremogram type. If type = 1, the upper tail extremogram is estimated. If type = 2, the lower tail extremogram is estimated. |
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 |
Value
Extremogram values and a plot (if requested).
References
Davis, R. A., Mikosch, T., & Cribben, I. (2012). Towards estimating extremal serial dependence via the bootstrapped extremogram. Journal of Econometrics,170(1), 142-152.
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
type = 1
maxlag = 70
df = 3
G = extremogram:::garchsim(omega,alpha,beta,n,df)
extremogram1(G, quant, maxlag, type, 1, 1, 0)
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 |
Value
Cross extremogram values and a plot (if requested).
References
Davis, R. A., Mikosch, T., & Cribben, I. (2012). Towards estimating extremal serial dependence via the bootstrapped extremogram. Journal of Econometrics,170(1), 142-152.
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)
Sample return time extremogram
Description
The function estimates the sample return time extremogram and creates an extremogram plot.
Usage
extremogramr(x, type, maxlag, uplevel = 1, lowlevel = 0, histogram = 1,
cutoff = 1)
Arguments
x |
Univariate time series (a vector). |
type |
Extremogram type. If type = 1, the upper tail extremogram is estimated. If type = 2, the lower tail extremogram is estimated. If type = 3, both upper and lower tail extremogram is estimated. |
maxlag |
Number of lags to include in the extremogram (an integer). |
uplevel |
Quantile of the time series to indicate a upper tail extreme event (a number between 0 and 1, default is 1). |
lowlevel |
Quantile of the time series to indicate a lower tail extreme event (a number between 0 and 1, default is 0). |
histogram |
An extremogram plot. If histogram = 1, a plot is created (default). If histogram = 0, no plot is created. |
cutoff |
The cutoff of the y-axis on the plot (a number between 0 and 1, default is 1). |
Value
Extremogram values, return time for extreme events, mean return time and a plot (if requested).
References
Davis, R. A., Mikosch, T., & Cribben, I. (2012). Towards estimating extremal serial dependence via the bootstrapped extremogram. Journal of Econometrics,170(1), 142-152.
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
uplevel = 0.95
lowlevel = 0.05
type = 3
maxlag = 70
df = 3
G = extremogram:::garchsim(omega,alpha,beta,n,df)
extremogramr(G, type, maxlag, uplevel, lowlevel, 1, 1)
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 |
exttype |
Extremogram type (see |
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 |
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
Davis, R. A., Mikosch, T., & Cribben, I. (2012). Towards estimating extremal serial dependence via the bootstrapped extremogram. Journal of Econometrics,170(1), 142-152.
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)
Confidence bands for the sample cross extremogram
Description
The function estimates empirical confidence bands for the sample cross extremogram via a permutation procedure under the assumption that the data are independent.
Usage
permfn2(x, p1, p2, m, type, exttype, maxlag, start = 1, alpha = 0.05)
Arguments
x |
Bivariate time series (n by 2 matrix). |
p1 |
Quantile of the first time series to indicate an extreme event (a number between 0 and 1). |
p2 |
Quantile of the second 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 |
exttype |
Extremogram type (see |
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 |
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 cross extremogram plot.
References
Davis, R. A., Mikosch, T., & Cribben, I. (2012). Towards estimating extremal serial dependence via the bootstrapped extremogram. Journal of Econometrics,170(1), 142-152.
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
exttype = 1
maxlag = 70
df = 3
type = 3
m = 10
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)
permfn2(data, quant, quant, m, type, exttype, maxlag, 1, 0.05)
Confidence bands for the sample return time extremogram
Description
The function estimates empirical confidence bands for the sample returt time extremogram via a permutation procedure under the assumption that the data are independent.
Usage
permfnr(x, m, type, exttype, maxlag, uplevel = 1, lowlevel = 0, start = 1,
alpha = 0.05)
Arguments
x |
Univariate time series (a vector). |
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 |
exttype |
Extremogram type (see |
maxlag |
Number of lags to include in the extremogram (an integer). |
uplevel |
Quantile of the time series to indicate a upper tail extreme event (a number between 0 and 1, default is 1). |
lowlevel |
Quantile of the time series to indicate a lower tail extreme event (a number between 0 and 1, default is 0). |
start |
The lag that the extremogram plots starts at (an integer not greater than |
alpha |
Significance level for the confidence bands (a number between 0 and 1, default is 0.05). |
References
Davis, R. A., Mikosch, T., & Cribben, I. (2012). Towards estimating extremal serial dependence via the bootstrapped extremogram. Journal of Econometrics,170(1), 142-152.
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
uplevel = 0.95
lowlevel = 0.05
exttype = 3
maxlag = 70
type = 3
m = 10
df = 3
G = extremogram:::garchsim(omega,alpha,beta,n,df)
extremogramr(G, type, maxlag, uplevel, lowlevel, 1, 1)
permfnr(G, m, type, exttype, maxlag, uplevel, lowlevel, 1, 0.05)