 # Chapter 3. Multivariate Volatility Models (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 3.1/3.2: Download stock prices in R Last updated August 2019

y=apply(log(p),2,diff)    # calculate returns
y = y[,1:2]          # consider first two stocks
y[,1] = y[,1]-mean(y[,1]) # subtract mean
y[,2] = y[,2]-mean(y[,2])
TT = dim(y)

##### Listing 3.1/3.2: Download stock prices in MATLAB Last updated August 2016

p = p(:,[1,2]);      % consider first two stocks
y = diff(log(p))*100;          % convert prices to returns
y(:,1)=y(:,1)-mean(y(:,1)); % subtract mean
y(:,2)=y(:,2)-mean(y(:,2));
T = length(y);


##### Listing 3.3/3.4: EWMA in R Last updated August 2019

## create a matrix to hold covariance matrix for each t
EWMA = matrix(nrow=TT,ncol=3)
lambda = 0.94
S = cov(y)           # initial (t=1) covar matrix
EWMA[1,] = c(S)[c(1,4,2)]      # extract var and covar
for (i in 2:dim(y)){
S = lambda*S+(1-lambda)*  y[i-1,] %*% t(y[i-1,])
EWMA[i,] = c(S)[c(1,4,2)]
}
EWMArho = EWMA[,3]/sqrt(EWMA[,1]*EWMA[,2]) # calculate correlations
print(tail(EWMArho))

##### Listing 3.3/3.4: EWMA in MATLAB Last updated June 2018

%% create a matrix to hold covariance matrix for each t
EWMA = nan(T,3);
lambda = 0.94;
S = cov(y);          % initial (t=1) covar matrix
EWMA(1,:) = S([1,4,2]);        % extract var and covar
for i = 2:T          % loop though the sample
S = lambda*S+(1-lambda)* y(i-1,:)'*y(i-1,:);
EWMA(i,:) = S([1,4,2]);    % convert matrix to vector
end
EWMArho = EWMA(:,3)./sqrt(EWMA(:,1).*EWMA(:,2)); % calculate correlations


##### Listing 3.5/3.6: GOGARCH in R Last updated August 2019

library(rmgarch)
spec = gogarchspec(mean.model = list(armaOrder = c(0, 0),
include.mean =FALSE),
variance.model = list(model = "sGARCH",
garchOrder = c(1,1)) ,
distribution.model =  "mvnorm"
)
fit = gogarchfit(spec = spec, data = y)
show(fit)

##### Listing 3.5/3.6: OGARCH in MATLAB Last updated August 2016

[par, Ht] = o_mvgarch(y,2, 1,1,1);
Ht = reshape(Ht,4,T)';
%% Ht comes from o_mvgarch as a 3D matrix, this transforms it into a 2D matrix
OOrho = Ht(:,3) ./ sqrt(Ht(:,1) .* Ht(:,4));
%% OOrho is a vector of correlations


##### Listing 3.7/3.8: DCC in R Last updated August 2019

xspec = ugarchspec(mean.model = list(armaOrder = c(0, 0), include.mean = FALSE))
uspec = multispec(replicate(2, xspec))
spec = dccspec(uspec = uspec, dccOrder = c(1, 1), distribution = 'mvnorm')
res = dccfit(spec, data = y)
H=res@mfit\$H
DCCrho=vector(length=dim(y))
for(i in 1:dim(y)){
DCCrho[i] =  H[1,2,i]/sqrt(H[1,1,i]*H[2,2,i])
}

##### Listing 3.7/3.8: DCC in MATLAB Last updated June 2022

%%The function 'dcc' in MFE toolbox currently cannot work in MATLAB R2022a.
%%The function 'dcc' use one MATLAB Optimization toolbox function 'fmincon'.
%%The changes of 'fmincon' cause this problem.
%%This block can work on Optimization 8.3
[p, lik, Ht] = dcc(y,1,1,1,1);
Ht = reshape(Ht,4,T)';
DCCrho = Ht(:,3) ./ sqrt(Ht(:,1) .* Ht(:,4));
%% DCCrho is a vector of correlations


##### Listing 3.9/3.10: Sample statistics in R Last updated August 2019

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

##### Listing 3.9/3.10: Correlation comparison in MATLAB Last updated June 2018

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