%% SARMA Error Model Without an Intercept
% This example shows how to specify a regression model with SARMA errors without a regression intercept.
% 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.
% Copyright 2015 The MathWorks, Inc.