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

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 original 2011 R code will not fully work on a recent R because there have been some changes to libraries. At least two R packages support estimating GARCH style models. rugarch by Alexios Ghalanos and fGarch. For our purposes there nothing to separate them but rugarch is regularly maintained, but fGarch appears not to be.

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 R Last updated August 2019

library(rugarch)
y=diff(log(p\$Index))*100
y=y-mean(y)
## We multiply returns by 100 and de-mean them
spec1 = ugarchspec(variance.model = list( garchOrder = c(1, 1)),
mean.model = list( armaOrder = c(0,0),include.mean = FALSE))
res1 = ugarchfit(spec = spec1, data = y)
spec2 = ugarchspec(variance.model = list( garchOrder = c(1, 0)),
mean.model = list( armaOrder = c(0,0),include.mean = FALSE))
res2 = ugarchfit(spec = spec2, data = y)
spec3 = ugarchspec(variance.model = list( garchOrder = c(1, 1)),
mean.model = list( armaOrder = c(0,0),include.mean = FALSE),
distribution.model = "std")
res3 = ugarchfit(spec = spec3, data = y)
## plot(res) shows various graphical analysis, works in command line

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

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 2.3/2.4: Advanced ARCH and GARCH estimation in R Last updated August 2019

library(rugarch)
## normal APARCH(1,1)
spec4 = ugarchspec(variance.model = list(model="apARCH", garchOrder = c(1, 1)),
mean.model = list( armaOrder = c(0,0),include.mean = FALSE))
res4 = ugarchfit(spec = spec4, data = y)
#show(res4)
spec5 = ugarchspec(variance.model = list(model="apARCH", garchOrder = c(1, 1)),
mean.model = list( armaOrder = c(0,0),include.mean = FALSE), fixed.pars=list(delta=2))
res5 = ugarchfit(spec = spec5, data = y)
show(res5)

##### 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)