# Chapter 2. Univariate Volatility Modeling (in MATLAB/Julia)

Copyright 2011 - 2019 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: https://www.gnu.org/licenses/.

The GARCH functionality in the econometric toolbox in Matlab is trying to be too clever, but can't deliver and could well be buggy. If you want to try that, here are the docs (estimate). Besides, it can only do univariate GARCH and so can't be used in Chapter 3. Kevin Sheppard's MFE toolbox is much better, while not as user friendly, it is much better written and is certainly more comprehensive. It can be downloaded here and the documentation here is quite detailed.

##### Listing 2.1/2.2: ARCH and GARCH estimation in MATLAB Last updated June 2018

p = csvread('index.csv', 1, 0);
y=diff(log(p))*100;
y=y-mean(y);
%% We multiply returns by 100 and de-mean them
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)

##### Listing 2.1/2.2: ARCH and GARCH estimation in Julia Last updated June 2018

## No package for ARCH/GARCH estimation as of June 2018
## We have a mini-package for estimating GARCH(1,1) and t-GARCH(1,1)
using CSV;
p = CSV.read("index.csv", nullable = false)
y = diff(log.(p[:,1]))*100
y = y - mean(y)
using FRFGarch;
## Ensure that the folder FRFGarch is in the folder returned when LOAD_PATH is keyed into Julia command line
## The package must be in ../FRFGarch/src/FRFGarch.jl
res = GARCHfit(y, "GARCH");
println(res.par)
res_t = GARCHfit(y, "t-GARCH");
println(res_t.par)
## GARCH estimation will be slightly different from other languages
## this is due to GARCHfit choosing initial conditional vol = sample vol


##### Listing 2.3/2.4: Advanced ARCH and GARCH estimation in MATLAB Last updated August 2016

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)

##### Listing 2.3/2.4: Advanced ARCH and GARCH estimation in Julia Last updated June 2018

## We use the same mini-package to estimate APARCH(1,1)
res_AP = GARCHfit(y, "APARCH");
println(res_AP.par)
## GARCH estimation will be slightly different from other languages
## this is due to GARCHfit choosing initial conditional vol = sample vol