beta_function: Beta function

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

Beta function

Description

Represents a tool able to accommodate various lag structures for the additional MIDAS variable observed each "low-frequency" period t. It can have a monotonically increasing, decreasing weighting scheme or a hump-shaped weighting scheme. The Beta function is:

\delta_k(\omega)=\frac{(k/K)^{\omega_1-1} (1-k/K)^{\omega_2-1}}{\sum_{j=1}^K (j/K)^{\omega_1-1}(1-j/K)^{\omega_2-1}}.

For additional details, see \insertCiteghysels_2007;textualrumidas.

Usage

beta_function(k, K, w1, w2)

Arguments

k	Lag of interest.
K	Number of (lagged) realizations to consider.
w1, w2	Parameters governing the weights of each k lag.

Value

The weights associated to each lag k, with k=1,\cdots,K.

References

\insertAllCited

Examples

# suppose to have four lags: 
# K<-4 
# w1<-1	# by setting w1=1, only a monotonically decreasing weighting scheme is allowed
	#(more recent observations weigh more)
# w2<-5
beta_function(1:4,K=4,w1=1,w2=5)

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