Matlab and Julia Chapter 2. Univariate Volatility Modeling

Chapter 2. Univariate Volatility Modeling

Matlab and Julia

Copyright 2011 - 2023 Jon Danielsson. This code is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This code is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. The GNU General Public License is available at: www.gnu.org/licenses.

% ARCH and GARCH estimation in MATLAB
p = csvread('index.csv', 1, 0);
y=diff(log(p))*100;
y=y-mean(y);
tarch(y,1,0,0);              % ARCH(1)
tarch(y,4,0,0);              % ARCH(4)
tarch(y,4,0,1);              % GARCH(4,1)
tarch(y,1,0,1);              % GARCH(1,1)
tarch(y,1,0,1,'STUDENTST');  % t-GARCH(1,1)

ARCH and GARCH estimation in Julia
using CSV, Statistics, DataFrames;
y = diff(log.(p[:,1]))*100
y = y .- mean(y)
using ARCHModels;
arch1 = fit(ARCH{1}, y; meanspec = NoIntercept);
println("ARCH(1) model:", "\n", arch1)
arch4 = fit(ARCH{4}, y; meanspec = NoIntercept);
println("ARCH(4) model:", "\n", arch4)
garch4_1 = fit(GARCH{1,4}, y; meanspec = NoIntercept);
println("GARCH(4,1) model:", "\n", garch4_1)
garch1_1 = fit(GARCH{1,1}, y; meanspec = NoIntercept);
println("GARCH(1,1) model:", "\n", garch1_1)
tgarch1_1 = fit(GARCH{1,1}, y; meanspec = NoIntercept, dist = StdT);
println("tGARCH(1,1) model:", "\n", tgarch1_1)


% Advanced ARCH and GARCH estimation in MATLAB
aparch(y,1,1,1);              % APARCH(1,1)
aparch(y,2,2,1);              % APARCH(2,1)
aparch(y,1,1,1,'STUDENTST');  % t-APARCH(1,1)

Advanced ARCH and GARCH estimation in Julia
leverage_garch1_1 = fit(TGARCH{1, 1,1}, y; meanspec = NoIntercept);
println("GARCH(1,1) with leverage effects model:", "\n", leverage_garch1_1)


Financial Risk Forecasting
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