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

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

% Copyright 2015 The MathWorks, Inc.


%% 
% Specify the regression model with ARMA(3,2) errors: 
%
% $$\begin{array}{l}{y_t} = {X_t}\left[ \begin{array}{l}2.5\\ - 0.6\end{array} \right] + {u_t}\\{u_t} = 0.7{u_{t - 1}} - 0.3{u_{t - 2}} + 0.1{u_{t - 3}} + {\varepsilon _t} + 0.5{\varepsilon _{t - 1}} + 0.2{\varepsilon _{t - 2}},\end{array}$$
%
% where $\varepsilon_t$ has a _t_ distribution with the default degrees of freedom
% and unit variance. 
Mdl = regARIMA('Intercept',0,'Beta',[2.5; -0.6],...
    'AR',{0.7, -0.3, 0.1},'MA',{0.5, 0.2},'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 $t_5$ distribution. 
Mdl.Distribution = struct('Name','t','DoF',5) 

%%
% You can simulate or forecast responses from |Mdl| 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.