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

    %% SARMA Error Model Without an Intercept  
% This example shows how to specify a regression model with SARMA errors
% without a regression intercept.   

% Copyright 2015 The MathWorks, Inc.


%% 
% Specify the default regression model with
% $\rm{SARMA}(1,1)\times(2,1,1)_4$ errors:
%
% $$\begin{array}{c}{y_t} = {X_t}\beta  + {u_t}\\\left( {1 - {a_1}L} \right)\left( {1 - {A_4}{L^4} - {A_8}{L^8}} \right)\left( {1 - {L^4}} \right){u_t} = \left( {1 + {b_1}L} \right)\left( {1 + {B_4}{L^4}} \right){\varepsilon _t}.\end{array}$$
%
Mdl = regARIMA('ARLags',1,'SARLags',[4, 8],...
    'Seasonality',4,'MALags',1,'SMALags',4,'Intercept',0) 

%%
% The name-value pair argument: 
%
% * |'ARLags',1| specifies which lags have nonzero coefficients in the nonseasonal
% autoregressive polynomial, so $a(L) = (1 - a_1L)$.  
% * |'SARLags',[4 8]| specifies which lags have nonzero coefficients in
% the seasonal autoregressive polynomial, so $A(L) = (1 - A_4L^4 - A_8L^8)$.  
% * |'MALags',1| specifies which lags have nonzero coefficients in the nonseasonal
% moving average polynomial, so $b(L) = (1 + b_1L)$.  
% * |'SMALags',4| specifies which lags have nonzero coefficients in the
% seasonal moving average polynomial, so $B(L) = (1 + B_4L^4)$.  
% * |'Seasonality',4| specifies the degree of seasonal integration and corresponds
% to $(1 - L^4)$.     
%
%%
% The software sets |Intercept| to 0, but all other parameters in |Mdl|
% are |NaN| values by default. 

%%
% Property |P| = _p_ + _D_ + $p_s$ + s = 1 + 0 + 8 + 4 = 13, and property
% |Q| = _q_ + $q_s$ = 1 + 4 = 5. Therefore, the software requires at least
% 13 presample observation to initialize |Mdl|.  

%% 
% Since |Intercept| is not a |NaN|, it is an equality constraint during
% estimation. In other words, if you pass |Mdl| and data into |estimate|,
% then |estimate| sets |Intercept| to 0 during estimation.  
%
% You can modify the properties of |Mdl| using dot notation. 
%
% Be aware that the regression model intercept (|Intercept|) is not identifiable
% in regression models with ARIMA errors. If you want to estimate |Mdl|,
% then you must set |Intercept| to a value using, for example, dot notation.
% Otherwise, |estimate| might return a spurious estimate of |Intercept|.