| Type: | Package |
| Title: | Estimating a (c)DCC-GARCH Model in Large Dimensions |
| Version: | 0.1.0 |
| Description: | Functions for Estimating a (c)DCC-GARCH Model in large dimensions based on a publication by Engle et,al (2017) <doi:10.1080/07350015.2017.1345683> and Nakagawa et,al (2018) <doi:10.3390/ijfs6020052>. This estimation method is consist of composite likelihood method by Pakel et al. (2014) http://paneldataconference2015.ceu.hu/Program/Cavit-Pakel.pdf and (Non-)linear shrinkage estimation of covariance matrices by Ledoit and Wolf (2004,2015,2016). (<doi:10.1016/S0047-259X(03)00096-4>, <doi:10.1214/12-AOS989>, <doi:10.1016/j.jmva.2015.04.006>). |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| Author: | Kei Nakagawa 
[aut, cre],
Mitsuyoshi Imamura [aut] |
| Maintainer: | Kei Nakagawa <kei.nak.0315@gmail.com> |
| LazyData: | TRUE |
| Imports: | stats, Rcpp(≥ 0.10.6), nlshrink |
| Depends: | R(≥ 3.0.2) |
| LinkingTo: | Rcpp(≥ 0.10.6),RcppArmadillo(≥ 0.2.34) |
| Suggests: | rugarch(≥ 1.0.0) |
| RoxygenNote: | 6.0.1 |
| NeedsCompilation: | yes |
| Packaged: | 2018-07-12 12:07:16 UTC; kei |
| Repository: | CRAN |
| Date/Publication: | 2018-07-12 18:50:03 UTC |
Package
Description
Functions for Estimating a (c)DCC-GARCH Model in large dimensions based on a publication by Engle et,al (2017) and Nakagawa et,al (2018). This estimation method is consist of composite likelihood method by Pakel et al. (2014) and (Non-)linear shrinkage estimation of covariance matrices by Ledoit and Wolf (2004,2015,2016).
Details
To estimate the covariance matrix in financial time series, it is necessary consider two important aspects: the cross section and the time series. With regard to the cross section, we have the difficulty of correcting the biases of the sample covariance matrix eigenvalues in a large number of time series. With regard to the time series aspect, we have to account for volatility clustering and time-varying correlations. This package is implemented the improved estimation of the covariance matrix based on the following publications:
Aielli, Gian Piero. (2013). Dynamic conditional correlation: on properties and estimation. Journal of Business & Economic Statistics 31: 282-99. <doi:10.1080/07350015.2013.771027>
Engle, Robert F. (2002). Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models. Journal of Business & Economic Statistics 20: 339-50. <doi:10.1198/073500102288618487>
Engle, Robert F, Olivier Ledoit, and Michael Wolf. (2017). Large dynamic covariance matrices. Journal of Business & Economic Statistics, 1-13. <doi:10.1080/07350015.2017.1345683>
Kei Nakagawa, Mitsuyoshi Imamura and Kenichi Yoshida. (2018). Risk-Based Portfolios with Large Dynamic Covariance Matrices. International Journal of Financial Studies, 6(2), 1-14. <doi:10.3390/ijfs6020052>
Ledoit, O. and Wolf, M. (2004). A well-conditioned estimator for large-dimensional covariance matrices. Journal of Multivariate Analysis, 88(2). <doi:10.1016/S0047-259X(03)00096-4>
Ledoit, O. and Wolf, M. (2012). Nonlinear shrinkage estimation of large-dimensional covariance matrices. Annals of Statistics, 40(2). <doi:10.1214/12-AOS989>
Ledoit, O. and Wolf, M. (2015). Spectrum estimation: a unified framework for covariance matrix estimation and PCA in large dimensions. Journal of Multivariate Analysis, 139(2). <doi:10.1016/j.jmva.2015.04.006>
Pakel, Cavit and Shephard, Neil and Sheppard, Kevin and Engle, Robert F. (2014). Fitting vast dimensional time-varying covariance models. Technical report <http://paneldataconference2015.ceu.hu/Program/Cavit-Pakel.pdf>
This function get the correlation matrix (Rt) of estimated cDCC-GARCH model.
Description
This function get the correlation matrix (Rt) of estimated cDCC-GARCH model.
Usage
cdcc_correlations(param, stdresids, uncR, ts)
Arguments
param |
cDCC-GARCH parameters(alpha,beta) |
stdresids |
matrix of standrdized(De-GARCH) residual returns (T by N) |
uncR |
unconditional correlation matrix of stdresids (N by N) |
ts |
ts how many time series are you taking |
Value
the correlation matrix (Rt) of estimated cDCC-GARCH model (T by N^2)
Note
Rt are vectorized values of the conditional correlation matrix(Rt) until time t(ts) for each row.
This function estimates the parameters(alpha,beta) and time-varying correlation matrices(Rt) of cDCC-GARCH model.
Description
This function estimates the parameters(alpha,beta) and time-varying correlation matrices(Rt) of cDCC-GARCH model.
Usage
cdcc_estimation(ini.para = c(0.05, 0.93), ht, residuals, method = c("COV",
"LS", "NLS"), ts = 1)
Arguments
ini.para |
initial cDCC-GARCH parameters(alpha,beta) of optimization |
ht |
matrix of conditional variance vectors |
residuals |
matrix of residual(de-mean) returns |
method |
shrinkage method of unconditional correlation matrix(Cov:sample,LS:Linear Shrinkage,NLS:NonLinear Shrinkage) |
ts |
ts how many time series are you taking(dufalut:1 latest value) |
Value
time-varying correlations(Rt) and the result of estimation
Note
Rt are vectorized values of the conditional correlation matrix(Rt) until time t(ts) for each row.
Examples
library(rugarch)
library(xdcclarge)
#load data
data(us_stocks)
n<-3
Rtn<-log(us_stocks[-1,1:n]/us_stocks[-nrow(us_stocks),1:n])
# Step 1:GARCH Parameter Estimation with rugarch
spec = ugarchspec()
mspec = multispec( replicate(spec, n = n) )
fitlist = multifit(multispec = mspec, data = Rtn)
ht<-sigma(fitlist)^2
residuals<-residuals(fitlist)
# Step 2:cDCC-GARCH Parameter Estimation with xdcclarge
cDCC<-cdcc_estimation(ini.para=c(0.05,0.93) ,ht ,residuals)
#Time varying correlation matrix Rt at time t
(Rt<-matrix(cDCC$cdcc_Rt,n,n))
## Not run:
#If you want Rt at time t-s,then
s<-10
cDCC<-cdcc_estimation(ini.para=c(0.05,0.93) ,ht ,residuals,ts = s)
matrix(cDCC$cdcc_Rt[s,],n,n)
## End(Not run)
This functions calculates numerical gradient of log-likelihood of cDCC-GARCH model.
Description
This functions calculates numerical gradient of log-likelihood of cDCC-GARCH model.
Usage
cdcc_gradient(param, ht, residuals, stdresids, uncR, d = 1e-05)
Arguments
param |
cDCC-GARCH parameters(alpha,beta) |
ht |
matrix of conditional variance vectors (T by N) |
residuals |
matrix of residual(de-mean) returns (T by N) |
stdresids |
matrix of standrdized(De-GARCH) residual returns (T by N) |
uncR |
unconditional correlation matrix of stdresids (N by N) |
d |
(log-lik(x+d) - log-lik(x))/d |
Value
numerical gradient of log-likelihood of cDCC-GARCH model(vector)
This function calculates log-likelihood of cDCC-GARCH model.
Description
This function calculates log-likelihood of cDCC-GARCH model.
Usage
cdcc_loglikelihood(param, ht, residuals, stdresids, uncR)
Arguments
param |
cDCC-GARCH parameters(alpha,beta) |
ht |
matrix of conditional variance vectors (T by N) |
residuals |
matrix of residual(de-mean) returns (T by N) |
stdresids |
matrix of standrdized(De-GARCH) residual returns (T by N) |
uncR |
unconditional correlation matrix of stdresids (N by N) |
Value
log-likelihood of cDCC-GARCH model (scaler)
This function optimizes log-likelihood of cDCC-GARCH model.
Description
This function optimizes log-likelihood of cDCC-GARCH model.
Usage
cdcc_optim(param, ht, residuals, stdresids, uncR)
Arguments
param |
cDCC-GARCH parameters(alpha,beta) |
ht |
matrix of conditional variance vectors (T by N) |
residuals |
matrix of residual(de-mean) returns (T by N) |
stdresids |
matrix of standrdized(De-GARCH) residual returns (T by N) |
uncR |
unconditional correlation matrix of stdresids (N by N) |
Value
results of optimization
This function get the correlation matrix (Rt) of estimated DCC-GARCH model.
Description
This function get the correlation matrix (Rt) of estimated DCC-GARCH model.
Usage
dcc_correlations(param, stdresids, uncR, ts)
Arguments
param |
DCC-GARCH parameters(alpha,beta) |
stdresids |
matrix of standrdized(De-GARCH) residual returns (T by N) |
uncR |
unconditional correlation matrix of stdresids (N by N) |
ts |
ts how many time series are you taking |
Value
the correlation matrix (Rt) of estimated DCC-GARCH model (T by N^2)
Note
Rt are vectorized values of the conditional correlation matrix(Rt) until time t(ts) for each row.
This function estimates the parameters(alpha,beta) and time-varying correlation matrices(Rt) of DCC-GARCH model.
Description
This function estimates the parameters(alpha,beta) and time-varying correlation matrices(Rt) of DCC-GARCH model.
Usage
dcc_estimation(ini.para = c(0.05, 0.93), ht, residuals, method = c("COV",
"LS", "NLS"), ts = 1)
Arguments
ini.para |
initial DCC-GARCH parameters(alpha,beta) of optimization |
ht |
matrix of conditional variance vectors |
residuals |
matrix of residual(de-mean) returns |
method |
shrinkage method of unconditional correlation matrix(Cov:sample,LS:Linear Shrinkage,NLS:NonLinear Shrinkage) |
ts |
ts how many time series are you taking(dufalut:1 latest value) |
Value
time-varying correlations(Rt) and the result of estimation
Note
Rt are vectorized values of the conditional correlation matrix(Rt) until time t(ts) for each row.
Examples
library(rugarch)
library(xdcclarge)
#load data
data(us_stocks)
n<-3
Rtn<-log(us_stocks[-1,1:n]/us_stocks[-nrow(us_stocks),1:n])
# Step 1:GARCH Parameter Estimation with rugarch
spec = ugarchspec()
mspec = multispec( replicate(spec, n = n) )
fitlist = multifit(multispec = mspec, data = Rtn)
ht<-sigma(fitlist)^2
residuals<-residuals(fitlist)
# Step 2:DCC-GARCH Parameter Estimation with xdcclarge
DCC<-dcc_estimation(ini.para=c(0.05,0.93) ,ht ,residuals)
#Time varying correlation matrix Rt at time t
(Rt<-matrix(DCC$dcc_Rt,n,n))
## Not run:
#If you want Rt at time t-s,then
s<-10
DCC<-dcc_estimation(ini.para=c(0.05,0.93) ,ht ,residuals,ts = s)
matrix(DCC$cdcc_Rt[s,],n,n)
## End(Not run)
This functions calculates numerical gradient of log-likelihood of DCC-GARCH model.
Description
This functions calculates numerical gradient of log-likelihood of DCC-GARCH model.
Usage
dcc_gradient(param, ht, residuals, stdresids, uncR, d = 1e-05)
Arguments
param |
DCC-GARCH parameters(alpha,beta) |
ht |
matrix of conditional variance vectors (T by N) |
residuals |
matrix of residual(de-mean) returns (T by N) |
stdresids |
matrix of standrdized(De-GARCH) residual returns (T by N) |
uncR |
unconditional correlation matrix of stdresids (N by N) |
d |
(log-lik(x+d) - log-lik(x))/d |
Value
numerical gradient of log-likelihood of DCC-GARCH model (vector)
This function calculates log-likelihood of DCC-GARCH model.
Description
This function calculates log-likelihood of DCC-GARCH model.
Usage
dcc_loglikelihood(param, ht, residuals, stdresids, uncR)
Arguments
param |
DCC-GARCH parameters(alpha,beta) |
ht |
matrix of conditional variance vectors (T by N) |
residuals |
matrix of residual(de-mean) returns (T by N) |
stdresids |
matrix of standrdized(De-GARCH) residual returns (T by N) |
uncR |
unconditional correlation matrix of stdresids (N by N) |
Value
log-likelihood of DCC-GARCH model (scaler)
This function optimizes log-likelihood of DCC-GARCH model.
Description
This function optimizes log-likelihood of DCC-GARCH model.
Usage
dcc_optim(param, ht, residuals, stdresids, uncR)
Arguments
param |
DCC-GARCH parameters(alpha,beta) |
ht |
matrix of conditional variance vectors (T by N) |
residuals |
matrix of residual(de-mean) returns (T by N) |
stdresids |
matrix of standrdized(De-GARCH) residual returns (T by N) |
uncR |
unconditional correlation matrix of stdresids (N by N) |
Value
results of optimization
the closing price data of us stocks in SP500 index from 2006-03-31 to 2014-03-31 from yahoo finance.
Description
the closing price data of us stocks in SP500 index from 2006-03-31 to 2014-03-31 from yahoo finance.
Format
A data frame with 2013 rows and 460 variables:
Source
Yahoo finance