exp_almon {rumidas}

Exponential Almon Lag

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. As in Ghysels et al. (2007), here the function form uses only two parameters:

\delta_k(\omega_1, \omega_2) = \frac{exp(\omega_{1}k + \omega_2 k^2)}{\sum_{k=1}^K exp(\omega_1 k + \omega_2 k^2)}.

For additional details, see Almon (1965) and Ghysels et al. (2007).

Usage

exp_almon(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

Almon S (1965). “The distributed lag between capital appropriations and expenditures.” Econometrica: Journal of the Econometric Society, 178–196. doi:10.2307/1911894.

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 # Note: the number of lags to consider
# w1<-1	
# w2<- -0.5 # by setting w2<0, the monotonically decreasing weighting scheme is used
exp_almon(1:4,K=4,w1=0.1,w2=-0.5)