rStar: Natural Rate of Interest

#------------------------------------------------------------------------------#
# 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))
}