midasr (version 0.9)

nealmon: Normalized Exponential Almon lag MIDAS coefficients

Description

Calculate normalized exponential Almon lag coefficients given the parameters and required number of coefficients.

Usage

nealmon(p, d, m)

Value

vector of coefficients

Arguments

p

parameters for Almon lag

d

number of the coefficients

m

the frequency, currently ignored.

Author

Virmantas Kvedaras, Vaidotas Zemlys

Details

Given unrestricted MIDAS regression

$$y_t=\sum_{h=0}^d\theta_{h}x_{tm-h}+\mathbf{z_t}\beta+u_t$$

normalized exponential Almon lag restricts the coefficients \(theta_h\) in the following way:

$$\theta_{h}=\delta\frac{\exp(\lambda_1(h+1)+\dots+ \lambda_r(h+1)^r)}{\sum_{s=0}^d\exp(\lambda_1(s+1)+\dots+\lambda_r(h+1)^r)}$$

The parameter \(\delta\) should be the first element in vector p. The degree of the polynomial is then decided by the number of the remaining parameters.

Examples

##Load data
data("USunempr")
data("USrealgdp")

y <- diff(log(USrealgdp))
x <- window(diff(USunempr),start=1949)
t <- 1:length(y)

midas_r(y~t+fmls(x,11,12,nealmon),start=list(x=c(0,0,0)))