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%% Default Regression Model with AR Errors % This example shows how to apply the shorthand |regARIMA(p,D,q)| syntax % to specify a regression model with AR errors. % Copyright 2015 The MathWorks, Inc. %% % Specify the default regression model with AR(3) errors: % % $$\begin{array}{l} {y_t} = c + {X_t}\beta + {u_t}\\ {u_t} = {a_1}{u_{t - 1}} + {a_2}{u_{t - 2}} + {a_3}{u_{t - 3}} + {\varepsilon _t}.\end{array}$$ % Mdl = regARIMA(3,0,0) %% % The software sets the innovation distribution to |Gaussian|, and each % parameter to |NaN|. The AR coefficients are at lags 1 through 3. %% % Pass |Mdl| into |estimate| with data to estimate the parameters set to % |NaN|. Though |Beta| is not in the display, if you pass a matrix of predictors % ($X_t$) into |estimate|, then |estimate| estimates |Beta|. The |estimate| % function infers the number of regression coefficients in |Beta| from the % number of columns in $X_t$. % % Tasks such as simulation and forecasting using |simulate| and |forecast| % do not accept models with at least one |NaN| for a parameter value. Use % dot notation to modify parameter values.