Package xdcclarge. R topics documented: July 12, Type Package
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1 Type Package Package xdcclarge July 12, 2018 Title Estimating a (c)dcc-garch Model in Large Dimensions Version Functions for Estimating a (c)dcc-garch Model in large dimensions based on a publication by Engle et,al (2017) <doi: / > and Nakagawa et,al (2018) <doi: /ijfs >. This estimation method is consist of composite likelihood method by Pakel et al. (2014) < Pakel.pdf> and (Non-)linear shrinkage estimation of covariance matrices by Ledoit and Wolf (2004,2015,2016). (<doi: /s x(03) >, <doi: /12-aos989>, <doi: /j.jmva >). License GPL (>= 2) Author Kei Nakagawa [aut, cre] (< Mitsuyoshi Imamura [aut] Maintainer Kei Nakagawa <kei.nak.0315@gmail.com> LazyData TRUE Imports stats, Rcpp(>= ), nlshrink Depends R(>= 3.0.2) LinkingTo Rcpp(>= ),RcppArmadillo(>= ) Suggests rugarch(>= 1.0.0) RoxygenNote NeedsCompilation yes Repository CRAN Date/Publication :50:03 UTC R topics documented: cdcc_correlations cdcc_estimation cdcc_gradient
2 2 cdcc_correlations cdcc_loglikelihood cdcc_optim dcc_correlations dcc_estimation dcc_gradient dcc_loglikelihood dcc_optim us_stocks xdcclarge Index 11 cdcc_correlations This function get the correlation matrix (Rt) of estimated cdcc- GARCH model. This function get the correlation matrix (Rt) of estimated cdcc-garch model. cdcc_correlations(, stdresids, uncr, ts) cdcc-garch eters(alpha,beta) ts ts how many time series are you taking 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.
3 cdcc_estimation 3 cdcc_estimation This function estimates the eters(alpha,beta) and time-varying correlation matrices(rt) of cdcc-garch model. This function estimates the eters(alpha,beta) and time-varying correlation matrices(rt) of cdcc-garch model. cdcc_estimation(ini.para = c(0.05, 0.93), ht, residuals, method = c("cov", "LS", "NLS"), ts = 1) ini.para ht residuals method ts initial cdcc-garch eters(alpha,beta) of optimization matrix of conditional variance vectors matrix of residual(de-mean) returns shrinkage method of unconditional correlation matrix(cov:sample,ls:linear Shrinkage,NLS:NonLinear Shrinkage) ts how many time series are you taking(dufalut:1 latest value) Note time-varying correlations(rt) and the result of estimation 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
4 4 cdcc_gradient 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) cdcc_gradient This functions calculates numerical gradient of log-likelihood of cdcc-garch model. This functions calculates numerical gradient of log-likelihood of cdcc-garch model. cdcc_gradient(, ht, residuals, stdresids, uncr, d = 1e-05) cdcc-garch eters(alpha,beta) d (log-lik(x+d) - log-lik(x))/d numerical gradient of log-likelihood of cdcc-garch model(vector)
5 cdcc_loglikelihood 5 cdcc_loglikelihood This function calculates log-likelihood of cdcc-garch model. This function calculates log-likelihood of cdcc-garch model. cdcc_loglikelihood(, ht, residuals, stdresids, uncr) cdcc-garch eters(alpha,beta) log-likelihood of cdcc-garch model (scaler) cdcc_optim This function optimizes log-likelihood of cdcc-garch model. This function optimizes log-likelihood of cdcc-garch model. cdcc_optim(, ht, residuals, stdresids, uncr) cdcc-garch eters(alpha,beta) results of optimization
6 6 dcc_estimation dcc_correlations This function get the correlation matrix (Rt) of estimated DCC- GARCH model. This function get the correlation matrix (Rt) of estimated DCC-GARCH model. dcc_correlations(, stdresids, uncr, ts) DCC-GARCH eters(alpha,beta) ts ts how many time series are you taking 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. dcc_estimation This function estimates the eters(alpha,beta) and time-varying correlation matrices(rt) of DCC-GARCH model. This function estimates the eters(alpha,beta) and time-varying correlation matrices(rt) of DCC-GARCH model. dcc_estimation(ini.para = c(0.05, 0.93), ht, residuals, method = c("cov", "LS", "NLS"), ts = 1)
7 dcc_estimation 7 ini.para ht residuals method ts initial DCC-GARCH eters(alpha,beta) of optimization matrix of conditional variance vectors matrix of residual(de-mean) returns shrinkage method of unconditional correlation matrix(cov:sample,ls:linear Shrinkage,NLS:NonLinear Shrinkage) ts how many time series are you taking(dufalut:1 latest 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)
8 8 dcc_loglikelihood dcc_gradient This functions calculates numerical gradient of log-likelihood of DCC-GARCH model. This functions calculates numerical gradient of log-likelihood of DCC-GARCH model. dcc_gradient(, ht, residuals, stdresids, uncr, d = 1e-05) DCC-GARCH eters(alpha,beta) d (log-lik(x+d) - log-lik(x))/d numerical gradient of log-likelihood of DCC-GARCH model (vector) dcc_loglikelihood This function calculates log-likelihood of DCC-GARCH model. This function calculates log-likelihood of DCC-GARCH model. dcc_loglikelihood(, ht, residuals, stdresids, uncr) DCC-GARCH eters(alpha,beta)
9 dcc_optim 9 log-likelihood of DCC-GARCH model (scaler) dcc_optim This function optimizes log-likelihood of DCC-GARCH model. This function optimizes log-likelihood of DCC-GARCH model. dcc_optim(, ht, residuals, stdresids, uncr) DCC-GARCH eters(alpha,beta) results of optimization us_stocks the closing price data of us stocks in SP500 index from to from yahoo finance. Format Source the closing price data of us stocks in SP500 index from to from yahoo finance. A data frame with 2013 rows and 460 variables: Yahoo finance
10 10 xdcclarge xdcclarge Package Details 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). 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: <doi: / > Engle, Robert F. (2002). Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models. Journal of Business & Economic Statistics 20: <doi: / > Engle, Robert F, Olivier Ledoit, and Michael Wolf. (2017). Large dynamic covariance matrices. Journal of Business & Economic Statistics, <doi: / > Kei Nakagawa, Mitsuyoshi Imamura and Kenichi Yoshida. (2018). Risk-Based Portfolios with Large Dynamic Covariance Matrices. International Journal of Financial Studies, 6(2), <doi: /ijfs > Ledoit, O. and Wolf, M. (2004). A well-conditioned estimator for large-dimensional covariance matrices. Journal of Multivariate Analysis, 88(2). <doi: /s x(03) > Ledoit, O. and Wolf, M. (2012). Nonlinear shrinkage estimation of large-dimensional covariance matrices. Annals of Statistics, 40(2). <doi: /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: /j.jmva > Pakel, Cavit and Shephard, Neil and Sheppard, Kevin and Engle, Robert F. (2014). Fitting vast dimensional time-varying covariance models. Technical report < Pakel.pdf>
11 Index cdcc_correlations, 2 cdcc_estimation, 3 cdcc_gradient, 4 cdcc_loglikelihood, 5 cdcc_optim, 5 dcc_correlations, 6 dcc_estimation, 6 dcc_gradient, 8 dcc_loglikelihood, 8 dcc_optim, 9 us_stocks, 9 xdcclarge, 10 xdcclarge-package (xdcclarge), 10 11
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Type Package Package My.stepwise June 29, 2017 Title Stepwise Variable Selection Procedures for Regression Analysis Version 0.1.0 Author International-Harvard Statistical Consulting Company
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A Non-Parametric Approach of Heteroskedasticity Robust Estimation of Vector-Autoregressive (VAR) Models
Journal of Finance and Investment Analysis, vol.1, no.1, 2012, 55-67 ISSN: 2241-0988 (print version), 2241-0996 (online) International Scientific Press, 2012 A Non-Parametric Approach of Heteroskedasticity
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