R/chowlin_likelihood.R

In TSdisaggregation: High-Dimensional Temporal Disaggregation

#' Likelihood function from Chow-Lin or Litterman temporal disaggregation.  
#' 
#' Used in disaggregation.R to find estimates of the optimal rho parameter. 
#' 
#' @param Y  		The low-frequency response series (n_l x 1 matrix).
#' @param X  		The aggregated high-frequency indicator series (n_l x p matrix).
#' @param vcov Aggregated variance-covariance matrix of Chow-Lin or Litterman residuals. 
#' @keywords chow lin litterman temporal disaggregation
#' @references
#' \insertAllCited{}
#' @importFrom Rdpack reprompt	
#' @importFrom stats lm rbinom rnorm

chowlin_likelihood <- function(Y,X,vcov) {
  
  n_l = dim(Y)[1]
  
  # Simplification and Cholesky factorization of the Sigma 
  
  Uchol <- chol(vcov)
  Lchol <- t(Uchol)
  
  # Preconditioning the variables
  
  X_F <- solve(Lchol) %*% X
  Y_F <- solve(Lchol) %*% Y
  
  # Estimate betaHat_0 using GLS assuming Sigma with rho
  
  betaHat <- solve(t(X_F) %*% X_F) %*% t(X_F) %*% Y_F 
  
  # Obtain the residuals using betaHat_0
  
  u_l_sim <- Y - X %*% betaHat
  
  # Preconditioning for the LF function
  
  u_l_sim_F <- solve(Lchol) %*% u_l_sim
  
  # Calculate the likelihood function
  
  LF <- -(n_l/2)*log(2*pi)-1/2*log(det(Lchol %*% Uchol)) - n_l/2 - n_l/2*log((t(u_l_sim_F) %*% u_l_sim_F)/n_l)
  
  return(LF)
  
}