Copyright 2016 Jon Danielsson. Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at. http://www.apache.org/licenses/LICENSE-2.0. Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.

The R code from 2011 runs unmodified, this just updates the end date. The Matlab code would not run, so these are new functions. The GARCH functionality in the econometric toolbox in Matlab can only do univatiate GARCH. Kevin Sheppard's MFE toolbox is well written and is certainly comprehensive. Its whats used below. It can be downloaded here and the documentation here is quite comprehensive.

Last edited: August 2016

```
library("tseries")
library(zoo)
p1 = get.hist.quote(instrument = "msft",start = "2000-01-01",end = "2016-08-30",quote="AdjClose")
p2 = get.hist.quote(instrument = "ibm", start = "2000-01-01",end = "2016-08-30",quote="AdjClose")
p = cbind(p1,p2)
y = diff(log(p))*100
y[,1] = y[,1]-mean(y[,1])
y[,2] = y[,2]-mean(y[,2])
TT = length(y[,1])
```

Last edited: August 2016

```
stocks =hist_stock_data('01012000','30082016','msft','ibm')
p1 = stocks(1).AdjClose(end:-1:1);
p2 = stocks(2).AdjClose(end:-1:1);
p = [p1 p2];
y = diff(log(p))*100;
y(:,1)=y(:,1)-mean(y(:,1));
y(:,2)=y(:,2)-mean(y(:,2));
T = length(y);
```

Last edited: AUgut 2016

```
EWMA = matrix(nrow=TT,ncol=3)
lambda = 0.94
S = cov(y)
EWMA[1,] = c(S)[c(1,4,2)]
for (i in 2:TT){
S = lambda * S + (1-lambda) * t(y[i-1]) %*% y[i-1]
EWMA[i,] = c(S)[c(1,4,2)]
}
EWMArho = EWMA[,3]/sqrt(EWMA[,1]*EWMA[,2])
```

Last edited: 2011

```
EWMA = nan(T,3);
lambda = 0.94
S = cov(y)
EWMA(1,:) = S([1,4,2]);
for i = 2:T
S = lambda * S + (1-lambda) * y(i,:)' * y(i,:)
EWMA(i,:) = S([1,4,2]);
end
EWMArho = EWMA(:,3) ./ sqrt(EWMA(:,1) .* EWMA(:,2))
```

Last edited: 2011

```
library(gogarch)
res = gogarch(y,formula = ~garch(1,1),garchlist = c(include.mean=FALSE))
OOrho = ccor(res)
```

Last edited: August 2016

```
[par, Ht] = o_mvgarch(y,2, 1,1,1);
Ht = reshape(Ht,4,T)';
OOrho = Ht(:,3) ./ sqrt(Ht(:,1) .* Ht(:,4));
```

Last edited: 2011

```
library(ccgarch)
f1 = garchFit(~ garch(1,1), data=y[,1],include.mean=FALSE)
f1 = f1@fit$coef
f2 = garchFit(~ garch(1,1), data=y[,2],include.mean=FALSE)
f2 = f2@fit$coef
a = c(f1[1], f2[1])
A = diag(c(f1[2],f2[2]))
B = diag(c(f1[3], f2[3]))
dccpara = c(0.2,0.6)
dccresults = dcc.estimation(inia=a, iniA=A, iniB=B, ini.dcc=dccpara,dvar=y, model="diagonal")
DCCrho = dccresults$DCC[,2]
```

Last edited: August 2016

```
[p, lik, Ht] = dcc(y,1,1,1,1)
Ht = reshape(Ht,4,T)';
DCCrho = Ht(:,3) ./ sqrt(Ht(:,1) .* Ht(:,4));
```

Last edited: 2011

```
matplot(cbind(EWMArho,DCCrho,OOrho),type='l',las=1,lty=1:3,col=1:3,ylab="")
mtext("Correlations",side=2,line=0.3,at=1,las=1,cex=0.8)
legend(2100,0,c("EWMA","DCC","OO"),lty=1:3,col=1:3,bty="n",cex=0.7)
```

Last edited: 2011

```
plot([EWMArho,OOrho,DCCrho])
legend('EWMA','DCC','OOrho','Location','SouthWest')
```

All rights reserved, Jon Danielsson, 2011-2016.