Obtains the log-likelihood of the GARCH-MIDAS-X, according to two errors' conditional distributions: Normal and Student-t. For details, see engle_ghysels_sohn_2013;textualrumidas and conrad_lock_2015;textualrumidas.
GM_X_loglik_no_skew(
param,
daily_ret,
X,
mv_m,
K,
distribution,
lag_fun = "Beta"
)
The resulting vector is the log-likelihood value for each
Vector of starting values.
Daily returns, which must be an "xts" object.
Additional "X" variable, which must be an "xts" object. Morever, "X" must be observed for the same days of daily_ret.
MIDAS variable already transformed into a matrix, through mv_into_mat
function.
Number of (lagged) realizations of the MIDAS variable to consider.
The conditional density to use for the innovations. At the moment, valid choices are "norm" and "std", for the Normal and Student-t distributions.
optional. Lag function to use. Valid choices are "Beta" (by default) and "Almon", for the Beta and Exponential Almon lag functions, respectively.
mv_into_mat
.
# \donttest{
# conditional density of the innovations: normal
start_val<-c(alpha=0.01,beta=0.8,z=0.1,m=0,theta=0.1,w2=2)
r_t<-sp500['2005/2010']
X<-rv5['2005/2010']^0.5
mv_m<-mv_into_mat(r_t,diff(indpro),K=12,"monthly")
sum(GM_X_loglik_no_skew(start_val,r_t,X,mv_m,K=12,distribution="norm"))
# conditional density of the innovations: Student-t
start_val<-c(alpha=0.01,beta=0.8,z=0.1,m=0,theta=0.1,w2=2,shape=5)
r_t<-sp500['2005/2010']
X<-rv5['2005/2010']^0.5
mv_m<-mv_into_mat(r_t,indpro,K=12,"monthly")
sum(GM_X_loglik_no_skew(start_val,r_t,X,mv_m,K=12,distribution="std"))
# }
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