GM_X_loglik_no_skew: GARCH-MIDAS-X log-likelihood (no skewness)

Description

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.

Usage

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

Value

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

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.

References

Examples

Run this code

# \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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