Copyright 2011 - 2020 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/.

Last updated July 2020

```
library(rugarch)
p = read.csv('index.csv')
## 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
```

Last updated July 2020

```
using CSV, Statistics;
p = CSV.read("index.csv")
y = diff(log.(p[:,1]))*100
y = y .- mean(y)
using ARCHModels;
## ARCH(1)
arch1 = fit(ARCH{1}, y; meanspec = NoIntercept);
println("ARCH(1) model:", "\n", arch1)
## ARCH(4)
arch4 = fit(ARCH{4}, y; meanspec = NoIntercept);
println("ARCH(4) model:", "\n", arch4)
## Note: Order of GARCH arguments here is reversed
## First argument: lags for sigma, second argument: lags for returns squared
## GARCH(4,1)
garch4_1 = fit(GARCH{1,4}, y; meanspec = NoIntercept);
println("GARCH(4,1) model:", "\n", garch4_1)
## GARCH(1,1)
garch1_1 = fit(GARCH{1,1}, y; meanspec = NoIntercept);
println("GARCH(1,1) model:", "\n", garch1_1)
## tGARCH(1,1)
tgarch1_1 = fit(GARCH{1,1}, y; meanspec = NoIntercept, dist = StdT);
println("tGARCH(1,1) model:", "\n", tgarch1_1)
```

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)
```

Last updated July 2020

```
leverage_garch1_1 = fit(TGARCH{1, 1,1}, y; meanspec = NoIntercept);
println("GARCH(1,1) with leverage effects model:", "\n", leverage_garch1_1)
## There is no package for apARCH estimation in Julia at present
```