%% Regression Model with MA Errors and t Innovations
% This example shows how to set the innovation distribution of a regression model with MA errors to a t distribution.
% Specify the regression model with MA(2) errors:
% \begin{array}{l}{y_t} = {X_t}\left[ \begin{array}{l}0.5\\ - 3\\1.2\end{array} \right] + {u_t}\\{u_t} = {\varepsilon _t} + 0.5{\varepsilon _{t - 1}} - 0.1{\varepsilon _{t - 2}},\end{array}
% where \varepsilon_t has a t distribution with the default degrees of freedom and unit variance.

Mdl = regARIMA('Intercept',0,'Beta',[0.5; -3; 1.2],...
    'MA',{0.5, -0.1},'Variance',1,'Distribution','t')

% The default degrees of freedom is NaN. If you don't know the degrees of freedom, then you can estimate it by passing Mdl and the data to estimate.
%
% Specify a t_{15} distribution.

Mdl.Distribution = struct('Name','t','DoF',15)

% You can simulate and forecast responses from by passing Mdl to simulate or forecast because Mdl is completely specified.
% In applications, such as simulation, the software normalizes the random t innovations. In other words, Variance overrides the theoretical variance of the t random variable (which is DoF/(DoF - 2)), but preserves the kurtosis of the distribution.
% Copyright 2015 The MathWorks, Inc.