www.gusucode.com > econ 案例源码程序 matlab代码 > econ/RegressionModelwithARErrorsandtInnovationsExample.m

    %% Regression Model with AR Errors and t Innovations  
% This example shows how to set the innovation distribution of a regression
% model with AR errors to a $t$ distribution.   

% Copyright 2015 The MathWorks, Inc.


%% 
% Specify the regression model with AR(4) errors:
%
% $$\begin{array}{l}{y_t} = {X_t}\left[ \begin{array}{l} - 2\\0.5\end{array} \right] + {u_t}\\{u_t} = 0.2{u_{t - 1}} + 0.1{u_{t - 4}} + {\varepsilon _t},\end{array}$$
%
% where $\varepsilon_t$ has a $t$ distribution with the default degrees of freedom
% and unit variance. 
Mdl = regARIMA('AR',{0.2,0.1},'ARLags',[1,4],...
    'Constant',0,'Beta',[-2;0.5],'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 $t_{10}$ distribution. 
Mdl.Distribution = struct('Name','t','DoF',10) 

%%
% You can simulate or forecast responses using |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.