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    %% Specify GARCH Model with t Innovation Distribution  
% This example shows how to specify a GARCH model with a Student's t innovation
% distribution.   

% Copyright 2015 The MathWorks, Inc.


%% 
% Specify a GARCH(1,1) model with a mean offset, 
%
% $$y_t = \mu + \varepsilon_t,$$
%
% where $\varepsilon_t = \sigma_t z_t$ and 
%
% $$\sigma _t^2 = \kappa  + {\gamma _1}\sigma _{t - 1}^2 + {\alpha _1}\varepsilon _{t - 1}^2.$$
%
% Assume $z_{t}$ follows a Student's t innovation distribution with eight
% degrees of freedom. 
tdist = struct('Name','t','DoF',8);
Mdl = garch('Offset',NaN,'GARCHLags',1,'ARCHLags',1,...
              'Distribution',tdist) 

%%
% The value of |Distribution| is a |struct| array with field |Name| equal
% to |'t'| and field |DoF| equal to |8|. When you specify the degrees of
% freedom, they aren't estimated if you input the model to |estimate|.