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    %% Regression Model with AR Errors  
% This example shows how to plot the impulse response function for a regression
% model with AR errors.   

% Copyright 2015 The MathWorks, Inc.


%% 
% Specify the regression model with AR(4) errors:
%
% $$\begin{array}{l}{y_t} = 2 + {X_t}\left[ \begin{array}{l}5\\ - 1\end{array} \right] + {u_t}\\{u_t} = 0.9{u_{t - 1}} - 0.8{u_{t - 2}} + 0.75{{\rm{u}}_{t - 3}} - 0.6{{\rm{u}}_{t - 4}} + {\varepsilon _t}.\end{array}$$
%
Mdl = regARIMA('Intercept',2,'Beta',[5; -1],'AR',...
    {0.9, -0.8, 0.75, -0.6}) 

%%
% The dynamic multipliers are absolutely summable because the autoregressive
% component is stable. Therefore, |Mdl| is stationary. 

%%
% You do not need to specify the innovation variance.  

%% 
% Plot the impulse response function. 
impulse(Mdl)    

%%
% The impulse response decays to 0 since |Mdl| defines a stationary error
% process. The regression component does not impact the impulse responses.