%% Seasonal ARIMA Model with Known Parameter Values
% This example shows how to specify a multiplicative seasonal ARIMA model (for quarterly data) with known parameter values. You can use such a fully specified model as an input to simulate or forecast.
% Specify the multiplicative seasonal ARIMA model
% (1 - .5L)(1 + 0.7{L^4}){(1 - L)^1}(1 - {L^4}){y_t} = (1 + .3L)(1 - .2{L^4}){\varepsilon _t},
% where the innovation distribution is Gaussian with constant variance 0.15. Here, (1 - L)^1 is the nonseasonal differencing operator and  (1 - L^4) is the first degree seasonal differencing operator with periodicity 4.

Mdl = arima('Constant',0,'AR',0.5,'D',1,'MA',0.3,...
    'Seasonality',4,'SAR',-0.7,'SARLags',4,...
    'SMA',-0.2,'SMALags',4,'Variance',0.15)

% The output specifies the nonseasonal and seasonal AR coefficients with opposite signs compared to the lag polynomials. This is consistent with the difference equation form of the model. The output specifies the lags of the seasonal AR and MA coefficients using SARLags and SMALags, respectively. D specifies the degree of nonseasonal integration. Seasonality = 4 specifies quarterly data with one degree of seasonal integration.
% All parameter values are specified, that is, no object property is NaN-valued.
% Copyright 2015 The MathWorks, Inc.