rumidas (version 0.1.3)

beta_function: 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_2007;textualrumidas.

Usage

beta_function(k, K, w1, w2)

Value

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

Arguments

k

Lag of interest.

K

Number of (lagged) realizations to consider.

w1, w2

Parameters governing the weights of each \(k\) lag.

References

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)