The GARCH functionality in the econometric toolbox in Matlab cannot do univariate GARCH.
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.
p = csvread('stocks.csv',1,0);
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);
using CSV;
p = CSV.read("stocks.csv",nullable=false);
y1 = diff(log.(p[:,1])).*100; # consider first two stocks
y2 = diff(log.(p[:,2])).*100; # convert prices to returns
y1 = y1-mean(y1); # subtract mean
y2 = y2-mean(y2);
y = hcat(y1,y2); # combine both series horizontally
T = size(y,1); # get the height of timeseries
%% 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
## create a matrix to hold covariance matrix for each t
EWMA = fill!(Array{Float64}(T,3), NaN)
lambda = 0.94
S = cov(y) # initial (t=1) covar matrix
EWMA[1,:] = [S[1], S[4], S[2]] # extract var and covar
for i in range(2,T-1) # loop though the sample
S = lambda*S+(1-lambda)*y[i-1,:]*(y[i-1,:])'
EWMA[i,:] = [S[1], S[4], S[2]] # convert matrix to vector
end
EWMArho = EWMA[:,3]./sqrt.(EWMA[:,1].*EWMA[:,2]) # calculate correlations
[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
## No OGARCH code available in Julia at present
[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
## No DCC code available in Julia at present
plot([EWMArho,OOrho,DCCrho])
legend('EWMA','DCC','OGARCH','Location','SouthWest')
## No OGARCH/DCC code available in Julia at present