R/compute_variance_decompositions.R

In bsvars: Bayesian Estimation of Structural Vector Autoregressive Models

#' @title Computes posterior draws of the forecast error variance decomposition
#'
#' @description Each of the draws from the posterior estimation of models from
#' packages \pkg{bsvars} or \pkg{bsvarSIGNs}
#' is transformed into a draw from the posterior distribution of the forecast error variance decomposition. 
#' 
#' @param posterior posterior estimation outcome obtained by running the \code{estimate} function. 
#' The interpretation depends on the normalisation of the shocks
#' using function \code{normalise_posterior()}. Verify if the default settings are appropriate.
#' @param horizon a positive integer number denoting the forecast horizon for 
#' the forecast error variance decomposition computations.
#' 
#' @return An object of class PosteriorFEVD, that is, an \code{NxNx(horizon+1)xS} array with attribute PosteriorFEVD 
#' containing \code{S} draws of the forecast error variance decomposition.
#'
#' @seealso \code{\link{compute_impulse_responses}}, \code{\link{estimate}}, \code{\link{normalise_posterior}}, \code{\link{summary}}
#'
#' @author Tomasz Woźniak \email{wozniak.tom@pm.me}
#' 
#' @references 
#' Kilian, L., & Lütkepohl, H. (2017). Structural VAR Tools, Chapter 4, In: Structural vector autoregressive analysis. Cambridge University Press.
#' 
#' @examples
#' # upload data
#' data(us_fiscal_lsuw)
#' 
#' # specify the model and set seed
#' set.seed(123)
#' specification  = specify_bsvar$new(us_fiscal_lsuw, p = 1)
#' 
#' # run the burn-in
#' burn_in        = estimate(specification, 10)
#' 
#' # estimate the model
#' posterior      = estimate(burn_in, 20)
#' 
#' # compute forecast error variance decomposition 2 years ahead
#' fevd           = compute_variance_decompositions(posterior, horizon = 8)
#' 
#' # workflow with the pipe |>
#' ############################################################
#' set.seed(123)
#' us_fiscal_lsuw |>
#'   specify_bsvar$new(p = 1) |>
#'   estimate(S = 10) |> 
#'   estimate(S = 20) |> 
#'   compute_variance_decompositions(horizon = 8) -> fevd
#' 
#' @export
compute_variance_decompositions <- function(posterior, horizon) {
  stopifnot("Argument horizon must be a positive integer number." = horizon > 0 & horizon %% 1 == 0)
  UseMethod("compute_variance_decompositions", posterior)
}




#' @inherit compute_variance_decompositions
#' @method compute_variance_decompositions PosteriorBSVAR
#' @description Each of the draws from the posterior estimation of the model
#' is transformed into a draw from the posterior distribution of the forecast 
#' error variance decomposition. 
#' @param posterior posterior estimation outcome - an object of class 
#' \code{PosteriorBSVAR} obtained by running the \code{estimate} function.
#' 
#' @export
compute_variance_decompositions.PosteriorBSVAR <- function(posterior, horizon) {

  posterior_B     = posterior$posterior$B
  posterior_A     = posterior$posterior$A
  N               = dim(posterior_A)[1]
  p               = posterior$last_draw$p
  S               = dim(posterior_A)[3]
  Y               = posterior$last_draw$data_matrices$Y
  
  posterior_irf   = .Call(`_bsvars_bsvars_ir`, posterior_B, posterior_A, horizon, p, TRUE)
  qqq             = .Call(`_bsvars_bsvars_fevd_homosk`, posterior_irf)

  fevd            = array(NA, c(N, N, horizon + 1, S), dimnames = list(rownames(Y), rownames(Y), 0:horizon, 1:S))
  for (s in 1:S) fevd[,,,s] = qqq[s][[1]]
  class(fevd)     = "PosteriorFEVD"

  return(fevd)
}





#' @inherit compute_variance_decompositions
#' @method compute_variance_decompositions PosteriorBSVARMSH
#' @description Each of the draws from the posterior estimation of the model
#' is transformed into a draw from the posterior distribution of the forecast 
#' error variance decomposition. In this heteroskedastic model the forecast error 
#' variance decompositions are computed for the forecasts with the origin at the
#' last observation in sample data and using the conditional variance forecasts.
#' @param posterior posterior estimation outcome - an object of class 
#' \code{PosteriorBSVARMSH} obtained by running the \code{estimate} function.
#' 
#' @examples
#' # upload data
#' data(us_fiscal_lsuw)
#' 
#' # specify the model and set seed
#' set.seed(123)
#' specification  = specify_bsvar_msh$new(us_fiscal_lsuw, p = 1, M = 2)
#' 
#' # run the burn-in
#' burn_in        = estimate(specification, 10)
#' 
#' # estimate the model
#' posterior      = estimate(burn_in, 20)
#' 
#' # compute forecast error variance decomposition 2 years ahead
#' fevd           = compute_variance_decompositions(posterior, horizon = 8)
#' 
#' # workflow with the pipe |>
#' ############################################################
#' set.seed(123)
#' us_fiscal_lsuw |>
#'   specify_bsvar_msh$new(p = 1, M = 2) |>
#'   estimate(S = 10) |> 
#'   estimate(S = 20) |> 
#'   compute_variance_decompositions(horizon = 8) -> fevd
#' 
#' @export
compute_variance_decompositions.PosteriorBSVARMSH <- function(posterior, horizon) {
  
  posterior_B     = posterior$posterior$B
  posterior_A     = posterior$posterior$A
  N               = dim(posterior_A)[1]
  p               = posterior$last_draw$p
  S               = dim(posterior_A)[3]
  T               = dim(posterior$posterior$xi)[2]
  posterior_PR_TR = posterior$posterior$PR_TR
  posterior_sigma2 = posterior$posterior$sigma2
  S_T             = posterior$posterior$xi[,T,]
  sigma2_T        = posterior$posterior$sigma[,T,]^2
  Y               = posterior$last_draw$data_matrices$Y

  posterior_irf   = .Call(`_bsvars_bsvars_ir`, posterior_B, posterior_A, horizon, p, TRUE)
  sigma2          = .Call(`_bsvars_forecast_sigma2_msh`, posterior_sigma2, posterior_PR_TR, S_T, horizon)
  qqq             = .Call(`_bsvars_bsvars_fevd_heterosk`, posterior_irf, sigma2, sigma2_T)
  
  fevd            = array(NA, c(N, N, horizon + 1, S), dimnames = list(rownames(Y), rownames(Y), 0:horizon, 1:S))
  for (s in 1:S) fevd[,,,s] = qqq[s][[1]]
  class(fevd)     = "PosteriorFEVD"
  
  return(fevd)
}









#' @inherit compute_variance_decompositions
#' @method compute_variance_decompositions PosteriorBSVARMIX
#' @description Each of the draws from the posterior estimation of the model
#' is transformed into a draw from the posterior distribution of the forecast 
#' error variance decomposition. In this mixture model the forecast error 
#' variance decompositions are computed for the forecasts with the origin at the
#' last observation in sample data and using the conditional variance forecasts.
#' @param posterior posterior estimation outcome - an object of class 
#' \code{PosteriorBSVARMIX} obtained by running the \code{estimate} function.
#' 
#' @examples
#' # upload data
#' data(us_fiscal_lsuw)
#' 
#' # specify the model and set seed
#' set.seed(123)
#' specification  = specify_bsvar_mix$new(us_fiscal_lsuw, p = 1, M = 2)
#' 
#' # run the burn-in
#' burn_in        = estimate(specification, 10)
#' 
#' # estimate the model
#' posterior      = estimate(burn_in, 20)
#' 
#' # compute forecast error variance decomposition 2 years ahead
#' fevd           = compute_variance_decompositions(posterior, horizon = 8)
#' 
#' # workflow with the pipe |>
#' ############################################################
#' set.seed(123)
#' us_fiscal_lsuw |>
#'   specify_bsvar_mix$new(p = 1, M = 2) |>
#'   estimate(S = 10) |> 
#'   estimate(S = 20) |> 
#'   compute_variance_decompositions(horizon = 8) -> fevd
#' 
#' @export
compute_variance_decompositions.PosteriorBSVARMIX <- function(posterior, horizon) {
  
  posterior_B     = posterior$posterior$B
  posterior_A     = posterior$posterior$A
  N               = dim(posterior_A)[1]
  p               = posterior$last_draw$p
  S               = dim(posterior_A)[3]
  T               = dim(posterior$posterior$xi)[2]
  posterior_PR_TR = posterior$posterior$PR_TR
  posterior_sigma2 = posterior$posterior$sigma2
  S_T             = posterior$posterior$xi[,T,]
  sigma2_T        = posterior$posterior$sigma[,T,]^2
  Y               = posterior$last_draw$data_matrices$Y

  posterior_irf   = .Call(`_bsvars_bsvars_ir`, posterior_B, posterior_A, horizon, p, TRUE)
  sigma2          = .Call(`_bsvars_forecast_sigma2_msh`, posterior_sigma2, posterior_PR_TR, S_T, horizon)
  qqq             = .Call(`_bsvars_bsvars_fevd_heterosk`, posterior_irf, sigma2, sigma2_T)
  
  fevd            = array(NA, c(N, N, horizon + 1, S), dimnames = list(rownames(Y), rownames(Y), 0:horizon, 1:S))
  for (s in 1:S) fevd[,,,s] = qqq[s][[1]]
  class(fevd)     = "PosteriorFEVD"
  
  return(fevd)
}



#' @inherit compute_variance_decompositions
#' @method compute_variance_decompositions PosteriorBSVARSV
#' @description Each of the draws from the posterior estimation of the model
#' is transformed into a draw from the posterior distribution of the forecast 
#' error variance decomposition. In this heteroskedastic model the forecast error 
#' variance decompositions are computed for the forecasts with the origin at the
#' last observation in sample data and using the conditional variance forecasts.
#' @param posterior posterior estimation outcome - an object of class 
#' \code{PosteriorBSVARSV} obtained by running the \code{estimate} function.
#' 
#' @examples
#' # upload data
#' data(us_fiscal_lsuw)
#' 
#' # specify the model and set seed
#' set.seed(123)
#' specification  = specify_bsvar_sv$new(us_fiscal_lsuw, p = 1)
#' 
#' # run the burn-in
#' burn_in        = estimate(specification, 10)
#' 
#' # estimate the model
#' posterior      = estimate(burn_in, 20)
#' 
#' # compute forecast error variance decomposition 2 years ahead
#' fevd           = compute_variance_decompositions(posterior, horizon = 8)
#' 
#' # workflow with the pipe |>
#' ############################################################
#' set.seed(123)
#' us_fiscal_lsuw |>
#'   specify_bsvar_sv$new(p = 1) |>
#'   estimate(S = 10) |> 
#'   estimate(S = 20) |> 
#'   compute_variance_decompositions(horizon = 8) -> fevd
#' 
#' @export
compute_variance_decompositions.PosteriorBSVARSV <- function(posterior, horizon) {
  
  posterior_B     = posterior$posterior$B
  posterior_A     = posterior$posterior$A
  N               = dim(posterior_A)[1]
  p               = posterior$last_draw$p
  S               = dim(posterior_A)[3]
  T               = dim(posterior$posterior$h)[2]
  posterior_h_T   = posterior$posterior$h[,T,]
  posterior_rho   = posterior$posterior$rho
  posterior_omega = posterior$posterior$omega
  centred_sv      = posterior$last_draw$centred_sv
  sigma2_T        = posterior$posterior$sigma[,T,]^2
  Y               = posterior$last_draw$data_matrices$Y

  posterior_irf   = .Call(`_bsvars_bsvars_ir`, posterior_B, posterior_A, horizon, p, TRUE)
  sigma2          = .Call(`_bsvars_forecast_sigma2_sv`, posterior_h_T, posterior_rho, posterior_omega, horizon, centred_sv)
  qqq             = .Call(`_bsvars_bsvars_fevd_heterosk`, posterior_irf, sigma2, sigma2_T)
  
  fevd            = array(NA, c(N, N, horizon + 1, S), dimnames = list(rownames(Y), rownames(Y), 0:horizon, 1:S))
  for (s in 1:S) fevd[,,,s] = qqq[s][[1]]
  class(fevd)     = "PosteriorFEVD"
  
  return(fevd)
}




#' @inherit compute_variance_decompositions
#' @method compute_variance_decompositions PosteriorBSVART
#' @description Each of the draws from the posterior estimation of the model
#' is transformed into a draw from the posterior distribution of the forecast 
#' error variance decomposition.
#' @param posterior posterior estimation outcome - an object of class 
#' \code{PosteriorBSVART} obtained by running the \code{estimate} function.
#' 
#' @examples
#' # upload data
#' data(us_fiscal_lsuw)
#' 
#' # specify the model and set seed
#' set.seed(123)
#' specification  = specify_bsvar_t$new(us_fiscal_lsuw)
#' 
#' # run the burn-in
#' burn_in        = estimate(specification, 10)
#' 
#' # estimate the model
#' posterior      = estimate(burn_in, 20)
#' 
#' # compute forecast error variance decomposition 2 years ahead
#' fevd           = compute_variance_decompositions(posterior, horizon = 8)
#' 
#' # workflow with the pipe |>
#' ############################################################
#' set.seed(123)
#' us_fiscal_lsuw |>
#'   specify_bsvar_t$new() |>
#'   estimate(S = 10) |> 
#'   estimate(S = 20) |> 
#'   compute_variance_decompositions(horizon = 8) -> fevd
#' 
#' @export
compute_variance_decompositions.PosteriorBSVART <- function(posterior, horizon) {
  
  posterior_B     = posterior$posterior$B
  posterior_A     = posterior$posterior$A
  posterior_df    = posterior$posterior$df
  p               = posterior$last_draw$p
  N               = dim(posterior_A)[1]
  S               = dim(posterior_A)[3]
  T               = dim(posterior$posterior$lambda)[1]
  sigma2          = array(NA, c(N, horizon, S))
  sigma2_T        = matrix(NA, N, S)
  Y               = posterior$last_draw$data_matrices$Y

  posterior_irf   = .Call(`_bsvars_bsvars_ir`, posterior_B, posterior_A, horizon, p, TRUE)
  lambda          = .Call(`_bsvars_forecast_lambda_t`, posterior_df, horizon) # (horizon, S)
  for (n in 1:N) {
    sigma2[n,,]   = lambda
    sigma2_T[n,]  = posterior$posterior$lambda[T,]
  }
  qqq             = .Call(`_bsvars_bsvars_fevd_heterosk`, posterior_irf, sigma2, sigma2_T)
  
  fevd            = array(NA, c(N, N, horizon + 1, S), dimnames = list(rownames(Y), rownames(Y), 0:horizon, 1:S))
  for (s in 1:S) fevd[,,,s] = qqq[s][[1]]
  class(fevd)     = "PosteriorFEVD"
  
  return(fevd)
}