cov_eval {dccmidas}

Var-cov matrix evaluation

Description

Evaluates the estimated var-cov matrix H_t with respect to a covariance proxy, under different robust loss functions (Laurent et al. 2013). The losses considered are also used in Amendola et al. (2020).

Usage

cov_eval(H_t, cov_proxy = NULL, r_t = NULL, loss = "FROB")

Arguments

H_t

Estimated covariance matrix, formatted as array

cov_proxy

optional Covariance matrix, formatted as array

r_t

optional List of daily returns used to calculate H_t. If parameter 'cov_proxy' is not provided, then r_t must be included. In this case, a (noise) proxy will be automatically used

loss

Robust loss function to use. Valid choices are: "FROB" for Frobenius (by default), "SFROB" for Squared Frobenius, "EUCL" for Euclidean, "QLIKE" for QLIKE and "RMSE" for Root Mean Squared Errors

Value

The value of the loss for each t

References

Amendola A, Braione M, Candila V, Storti G (2020). “A Model Confidence Set approach to the combination of multivariate volatility forecasts.” International Journal of Forecasting, 36(3), 873 - 891. doi:10.1016/j.ijforecast.2019.10.001.

Laurent S, Rombouts JV, Violante F (2013). “On loss functions and ranking forecasting performances of multivariate volatility models.” Journal of Econometrics, 173(1), 1–10. doi:10.1016/j.jeconom.2012.08.004.

Examples

require(xts)
# close to close daily log-returns
r_t_s<-diff(log(sp500['2010/2019'][,3]))
r_t_s[1]<-0
r_t_n<-diff(log(nasdaq['2010/2019'][,3]))
r_t_n[1]<-0
r_t_f<-diff(log(ftse100['2010/2019'][,3]))
r_t_f[1]<-0
db_m<-merge.xts(r_t_s,r_t_n,r_t_f)
db_m<-db_m[complete.cases(db_m),]
colnames(db_m)<-c("S&P500","NASDAQ","FTSE100")
# list of returns
r_t<-list(db_m[,1],db_m[,2],db_m[,3])
# estimation
K_c<-144
N_c<-36
cdcc_est<-dcc_fit(r_t,univ_model="sGARCH",distribution="norm",
corr_model="DCCMIDAS",N_c=N_c,K_c=K_c)
cov_eval(cdcc_est$H_t,r_t=r_t)[(K_c+1):dim(cdcc_est$H_t)[3]]