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    %% Simulate and Filter Disturbance Path Through GARCH Model

% Copyright 2015 The MathWorks, Inc.


%% 
% Specify a GARCH(1,1) model with Gaussian innovations. 
Mdl = garch('Constant',0.005,'GARCH',0.8,'ARCH',0.1);  

%% 
% Simulate the model using Monte Carlo simulation. Then, standardize the
% simulated innovations and filter them. 
rng(1); % For reproducibility
[v,e] = simulate(Mdl,100,'E0',0,'V0',0.05);
Z = e./sqrt(v);
[V,E] = filter(Mdl,Z,'Z0',0,'V0',0.05);  

%% 
% Confirm that the outputs of |simulate| and |filter| are identical. 
isequal(v,V) 

%%
% The logical value |1| confirms that the two outputs are identical.