Mary Mertzanidou and Theodore Panagiotidis 1.0 2026-09-16 News Impact Curves for GARCH and GJR-GARCH ts finance volatility This package draws the News Impact Curves (NIC) for a GARCH(1,1) and a GJR-GARCH(1,1) model on the same graph. Implements the analytical NIC formulas from: Engle, R.F. and Ng, V.K. (1993). Measuring and testing the impact of news on volatility. Journal of Finance, 48(5), 1749-1778. Both models must first be estimated with the gig package (this package requires gig to be installed), with AR lags = 1. This package provides one public function: nic_plot_from_gig(mod_garch, mod_gjr) Takes two gig bundles (a GARCH(1,1), type 1, and a GJR-GARCH(1,1), type 3) and plots both News Impact Curves on the same graph. Parameters: mod_garch : gig bundle holding a fitted GARCH(1,1) model (gig type = 1, estimated with AR lags = 1). mod_gjr : gig bundle holding a fitted GJR-GARCH(1,1) model (gig type = 3, estimated with AR lags = 1). NIC formulas (Engle and Ng, 1993): GARCH: h(e) = A + alpha * e^2 GJR (e >= 0): h(e) = A + alpha * e^2 GJR (e < 0): h(e) = A + (alpha + gamma) * e^2 where A = omega + beta * hbar and hbar = omega / (1 - alpha - beta) Printed output: Each call also prints the estimated coefficients and derived NIC quantities for both models to the console: omega : constant term in the variance equation alpha : coefficient on the squared shock (ARCH term) gamma : (GJR only) extra coefficient applied when the shock is negative, captures the leverage/asymmetry effect beta : coefficient on lagged conditional variance (GARCH term) hbar : the model's implied long-run (unconditional) variance A : the NIC curve's baseline height at e_{t-1} = 0 gig GARCH(1,1) bundle from gig (type 1) GJR-GARCH(1,1) bundle from gig (type 3) # --- extract GARCH coefficients --- matrix cg = mod_garch.coeff scalar g_omega = cg[3] scalar g_alpha = cg[4] scalar g_beta = cg[6] scalar g_hbar = g_omega / (1 - g_alpha - g_beta) scalar g_A = g_omega + g_beta * g_hbar # --- extract GJR coefficients --- matrix cgjr = mod_gjr.coeff scalar gjr_omega = cgjr[3] scalar gjr_alpha = cgjr[4] scalar gjr_gamma = cgjr[5] scalar gjr_beta = cgjr[6] scalar gjr_hbar = gjr_omega / (1 - gjr_alpha - gjr_beta) scalar gjr_A = gjr_omega + gjr_beta * gjr_hbar # --- print for verification --- printf "\n--- GARCH(1,1) ---\n" printf " omega = %.6e\n", g_omega printf " alpha = %.6e\n", g_alpha printf " beta = %.6e\n", g_beta printf " hbar = %.6e\n", g_hbar printf " A = %.6e\n", g_A printf "\n--- GJR-GARCH(1,1) ---\n" printf " omega = %.6e\n", gjr_omega printf " alpha = %.6e\n", gjr_alpha printf " gamma = %.6e\n", gjr_gamma printf " beta = %.6e\n", gjr_beta printf " hbar = %.6e\n", gjr_hbar printf " A = %.6e\n\n", gjr_A # --- plot --- string fname = sprintf("%snic_combined.gp", $dotdir) set force_decpoint on outfile @fname printf "set encoding utf8\n" printf "set linetype 1 lc rgb '#0072B2' lw 2.5\n" printf "set linetype 2 lc rgb '#D55E00' lw 2.5\n" printf "set title 'News Impact Curves - GARCH(1,1) vs GJR-GARCH(1,1)'\n" printf "set xlabel 'Standardised Residual (e_{t-1})'\n" printf "set ylabel 'Conditional Variance h_t'\n" printf "set xzeroaxis lt -1 lw 1 lc rgb '#808080'\n" printf "set border 15\n" printf "set grid\n" printf "set key left top\n" printf "set xrange [-3:3]\n\n" printf "garch_nic(x) = %g + %g*x**2\n", g_A, g_alpha printf "gjr_nic(x) = (x < 0) ? %g + %g*x**2 : %g + %g*x**2\n", gjr_A, gjr_alpha+gjr_gamma, gjr_A, gjr_alpha printf "plot garch_nic(x) title 'GARCH(1,1)' w lines lt 1, \\\n" printf " gjr_nic(x) title 'GJR-GARCH(1,1)' w lines lt 2\n" end outfile gnuplot --input=@fname --output=display include nic_gig.gfn include gig.gfn open nysewk setobs 52 1966-01-05 --time-series StockPrices = close Stock = interpol(StockPrices) StockReturns = ldiff(Stock) smpl +1 ; bundle mod_g = gig_setup(StockReturns, 1, const, null, 1) gig_estimate(&mod_g, 0) bundle mod_gjr = gig_setup(StockReturns, 3, const, null, 1) gig_estimate(&mod_gjr, 0) # Plot NICs nic_plot_from_gig(mod_g, mod_gjr)