GM_X_loglik: GARCH-MIDAS-X log-likelihood (with skewness)

In rumidas: Univariate GARCH-MIDAS, Double-Asymmetric GARCH-MIDAS and MEM-MIDAS

GARCH-MIDAS-X log-likelihood (with skewness)

Description

Obtains the log-likelihood of the GARCH-MIDAS-X, with an asymmetric term linked to past negative returns, according to two errors' conditional distributions: Normal and Student-t. For details, see \insertCiteengle_ghysels_sohn_2013;textualrumidas and \insertCiteconrad_lock_2015;textualrumidas.

Usage

GM_X_loglik(param, daily_ret, X, mv_m, K, distribution, lag_fun = "Beta")

Arguments

param	Vector of starting values.
daily_ret	Daily returns, which must be an "xts" object.
X	Additional "X" variable, which must be an "xts" object. Morever, "X" must be observed for the same days of daily_ret.
mv_m	MIDAS variable already transformed into a matrix, through mv_into_mat function.
K	Number of (lagged) realizations of the MIDAS variable to consider.
distribution	The conditional density to use for the innovations. At the moment, valid choices are "norm" and "std", for the Normal and Student-t distributions.
lag_fun	optional. Lag function to use. Valid choices are "Beta" (by default) and "Almon", for the Beta and Exponential Almon lag functions, respectively.

Value

The resulting vector is the log-likelihood value for each i,t.

References

\insertAllCited

See Also

mv_into_mat.

Examples

# conditional density of the innovations: normal
start_val<-c(alpha=0.01,beta=0.8,gamma=0.05,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(start_val,r_t,X=X,mv_m,K=12,distribution="norm"))

# conditional density of the innovations: Student-t
start_val<-c(alpha=0.01,beta=0.8,gamma=0.05,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,diff(indpro),K=12,"monthly")
sum(GM_X_loglik(start_val,r_t,X=X,mv_m,K=12,distribution="std"))

rumidas documentation built on April 4, 2025, 1:01 a.m.