#------------------------------------------------------------------------------#
# File: unpack.parameters.stage1.R
#
# Description: This file generates coefficient matrices for the stage 1
# state-space model for the given parameter vector.
#
# Stage 1 parameter vector: [a_y,1, a_y,2, b_pi, b_y, g, sigma_y~, sigma_pi, sigma_y*]
#------------------------------------------------------------------------------#
unpack.parameters.stage1 <- function(parameters, y.data, x.data, xi.00, P.00) {
A <- matrix(0, 4, 2)
A[1:2, 1] <- parameters[1:2] # a_y,1, a_y,2
A[1, 2] <- parameters[4] # b_y
A[3, 2] <- parameters[3] # b_pi
A[4, 2] <- 1-parameters[3] # 1 - b_pi
H <- matrix(0, 3, 2)
H[1, 1] <- 1
H[2:3, 1] <- -parameters[1:2] # -a_y,1, -a_y,2
H[2, 2] <- -parameters[4] # -b_y
R <- diag(c(parameters[6]^2, parameters[7]^2)) # sigma_y~, sigma_pi
Q <- matrix(0, 3, 3)
Q[1, 1] <- parameters[8]^2 # sigma_y*
F_matrix <- matrix(0, 3, 3)
F_matrix[1, 1] <- F_matrix[2, 1] <- F_matrix[3, 2] <- 1
# Make the data stationary
y.data[, 1] <- y.data[, 1] - 1:dim(y.data)[1] * parameters[5] # g
x.data[, 1] <- x.data[, 1] - 0:(dim(x.data)[1]-1) * parameters[5]
x.data[, 2] <- x.data[, 2] - -1:(dim(x.data)[1]-2) * parameters[5]
return(list("xi.00"=xi.00, "P.00"=P.00, "F_matrix"=F_matrix, "Q"=Q, "A"=A, "H"=H, "R"=R, "x.data"=x.data, "y.data"=y.data))
}
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