beta_function {rumidas}

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 Ghysels et al. (2007).

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

Ghysels E, Sinko A, Valkanov R (2007). “MIDAS regressions: Further results and new directions.” Econometric Reviews, 26(1), 53–90. doi:10.1080/07474930600972467.

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)