%% data
tsc=yahoo_prices({'GOOG'},'30-Sep-2009','30-Sep-2011');
prices=tsc.GOOG.Data(not(isnan(tsc.GOOG.Data))); % adjusted close prices
returns=log(prices(2:end)./prices(1:end-1)); % compound returns
%% Gosset student-t density
% theta(1) is location, theta(2) is scale, nu is shape
density=@(x,theta,nu)gamma(nu/2+1/2)/gamma(nu/2)/gamma(1/2)/sqrt(nu)...
    *(1+((x-theta(1))./theta(2)).^2/nu).^(-nu/2-1/2)/theta(2);
%% likelihood
logLikelihood=@(returns,theta,nu)sum(log(density(returns,theta,nu)));
estimate=@(nu)fminsearch(@(theta)-logLikelihood(returns,theta,nu),[0.0 0.01]);
%% plot
fplot(@(nu)logLikelihood(returns,estimate(nu),nu),[1 10])