# Historical Decompositions ```r HD(results, cri = 0.95) ``` ## Arguments - `results`: List containing the results from running BH_SBVAR(). - `cri`: credibility intervals for the estimates to be returned (default = 0.95). A value of 0.95 will return 95% credibility intervals. A value of 0.90 will return 90% credibility intervals. ## Returns An array containing historical decomposition estimates. ## Details Computes historical decomposition estimates. ## Examples ```r # Import data library(BHSBVAR) set.seed(123) data(USLMData) y0 <- matrix(data = c(USLMData$Wage, USLMData$Employment), ncol = 2) y <- y0 - (matrix(data = 1, nrow = nrow(y0), ncol = ncol(y0)) %*% diag(x = colMeans(x = y0, na.rm = FALSE, dims = 1))) colnames(y) <- c("Wage", "Employment") # Set function arguments nlags <- 8 itr <- 5000 burn <- 0 thin <- 1 acc <- TRUE h <- 20 cri <- 0.95 # Priors for A pA <- array(data = NA, dim = c(2, 2, 8)) pA[, , 1] <- c(0, NA, 0, NA) pA[, , 2] <- c(1, NA, -1, NA) pA[, , 3] <- c(0.6, 1, -0.6, 1) pA[, , 4] <- c(0.6, NA, 0.6, NA) pA[, , 5] <- c(3, NA, 3, NA) pA[, , 6] <- c(NA, NA, NA, NA) pA[, , 7] <- c(NA, NA, 1, NA) pA[, , 8] <- c(2, NA, 2, NA) # Position priors for Phi pP <- matrix(data = 0, nrow = ((nlags * ncol(pA)) + 1), ncol = ncol(pA)) pP[1:nrow(pA), 1:ncol(pA)] <- diag(x = 1, nrow = nrow(pA), ncol = ncol(pA)) # Confidence in the priors for Phi x1 <- matrix(data = NA, nrow = (nrow(y) - nlags), ncol = (ncol(y) * nlags)) for (k in 1:nlags) { x1[, (ncol(y) * (k - 1) + 1):(ncol(y) * k)] <- y[(nlags - k + 1):(nrow(y) - k),] } x1 <- cbind(x1, 1) colnames(x1) <- c(paste(rep(colnames(y), nlags), "_L", sort(rep(seq(from = 1, to = nlags, by = 1), times = ncol(y)), decreasing = FALSE), sep = ""), "cons") y1 <- y[(nlags + 1):nrow(y),] ee <- matrix(data = NA, nrow = nrow(y1), ncol = ncol(y1)) for (i in 1:ncol(y1)) { xx <- cbind(x1[, seq(from = i, to = (ncol(x1) - 1), by = ncol(y1))], 1) yy <- matrix(data = y1[, i], ncol = 1) phi <- solve(t(xx) %*% xx, t(xx) %*% yy) ee[, i] <- yy - (xx %*% phi) } somega <- (t(ee) %*% ee) / nrow(ee) lambda0 <- 0.2 lambda1 <- 1 lambda3 <- 100 v1 <- matrix(data = (1:nlags), nrow = nlags, ncol = 1) v1 <- v1^((-2) * lambda1) v2 <- matrix(data = diag(solve(diag(diag(somega)))), ncol = 1) v3 <- kronecker(v1, v2) v3 <- (lambda0^2) * rbind(v3, (lambda3^2)) v3 <- 1 / v3 pP_sig <- diag(x = 1, nrow = nrow(v3), ncol = nrow(v3)) diag(pP_sig) <- v3 # Confidence in long-run restriction priors pR_sig <- array(data = 0, dim = c(((nlags * ncol(y)) + 1), ((nlags * ncol(y)) + 1), ncol(y))) Ri <- cbind(kronecker(matrix(data = 1, nrow = 1, ncol = nlags), matrix(data = c(1, 0), nrow = 1)), 0) pR_sig[, , 2] <- (t(Ri) %*% Ri) / 0.1 # Confidence in priors for D kappa1 <- matrix(data = 2, nrow = 1, ncol = ncol(y)) # Set graphical parameters par(cex.axis = 0.8, cex.main = 1, font.main = 1, family = "serif", mfrow = c(2, 2), mar = c(2, 2.2, 2, 1), las = 1) # Estimate the parameters of the model results1 <- BH_SBVAR(y = y, nlags = nlags, pA = pA, pP = pP, pP_sig = pP_sig, pR_sig = pR_sig, kappa1 = kappa1, itr = itr, burn = burn, thin = thin, cri = cri) hd <- HD(results = results1, cri = cri) # Plot historical decompositions varnames <- colnames(USLMData)[2:3] shocknames <- c("Labor Demand","Labor Supply") freq <- 4 start_date <- c(floor(USLMData[(nlags + 1), 1]), round(((USLMData[(nlags + 1), 1] %% 1) * freq), digits = 0)) hd_results <- HD_Plots(results = hd, varnames = varnames, shocknames = shocknames, freq = freq, start_date = start_date) ``` ## Author(s) Paul Richardson

HD function