%% Specify the Default Regression Model with ARIMA Errors
% This example shows how to specify the default regression model with ARIMA errors using the shorthand ARIMA(p, D, q) notation corresponding to the following equation:
% \begin{array}{c} {y_t} = c + {u_t}\\ \left( {1 - {\phi _1}L - {\phi _2}{L^2} - {\phi _3}{L^3}} \right){\left( {1 - L} \right)^D}{u_t} = \left( {1 + {\theta _1}L + {\theta _2}{L^2}} \right){\varepsilon _t}.\end{array}
% Specify a regression model with ARIMA(3,1,2) errors.

Mdl = regARIMA(3,1,2)

% The model specification for Mdl appears in the Command Window. By default, regARIMA sets:
% The autoregressive (AR) parameter values to NaN at lags [1 2 3]
% The moving average (MA) parameter values to NaN at lags [1 2]
% The variance (Variance) of the innovation process, \varepsilon_t, to NaN
% The distribution (Distribution) of \varepsilon_t to Gaussian
% The regression model intercept to NaN
% There is no regression component (Beta) by default.
% The property:
% P = p + D, which represents the number of presample observations that the software requires to initialize the autoregressive component of the model to perform, for example, estimation.
% D represents the level of nonseasonal integration.
% Q represents the number of presample observations that the software requires to initialize the moving average component of the model to perform, for example, estimation.
% Fit Mdl to data by passing it and the data into estimate. If you pass the predictor series into estimate, then estimate estimates Beta by default.
% You can modify the properties of Mdl using dot notation.
% References:
% Box, G. E. P., G. M. Jenkins, and G. C. Reinsel. Time Series Analysis: Forecasting and Control. 3rd ed. Englewood Cliffs, NJ: Prentice Hall, 1994.
% Copyright 2015 The MathWorks, Inc.