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

Copyright 2011 - 2022 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/.

##### Listing 2.1/2.2: ARCH and GARCH estimation in R Last updated July 2020

library(rugarch)
## We multiply returns by 100 and de-mean them
y=diff(log(p\$Index))*100
y=y-mean(y)
## GARCH(1,1)
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)
## ARCH(1)
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)
## tGARCH(1,1)
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 July 2020

## 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)
## Normal APARCH(1,1) with fixed delta
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)