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    %% Default ARIMA Model  
% This example shows how to use the shorthand |arima(p,D,q)| syntax to specify
% the default ARIMA(_p_, _D_, _q_) model,  
%
% $${\Delta ^D}{y_t} = c + {\phi _1}{\Delta ^D}{y_{t - 1}} +  \ldots  + {\phi _p}{\Delta ^D}{y_{t - p}} + {\varepsilon _t} + {\theta _1}{\varepsilon _{t - 1}} +  \ldots  + {\theta _q}{\varepsilon _{t - q}},$$
%
% where ${\Delta ^D}{y_t}$ is a $D^{th}$ differenced
% time series. You can write this model in condensed form using lag operator
% notation:  
%
% $$\phi (L){(1 - L)^D}{y_t} = c + \theta (L){\varepsilon _t}.$$
%
% By default, all parameters in the created model object have unknown values,
% and the innovation distribution is Gaussian with constant variance.   

% Copyright 2015 The MathWorks, Inc.


%% 
% Specify the default ARIMA(1,1,1) model: 
model = arima(1,1,1) 

%%
% The output shows that the created model object, |model|, has |NaN| values for
% all model parameters: the constant term, the AR and MA coefficients, and
% the variance. You can modify the created model using dot notation,
% or input it (along with data) to |estimate|. 

%%
% The property |P| has value 2 (_p_ + _D_). This is the number of presample
% observations needed to initialize the AR model.