%% Default ARIMA Model
% This example shows how to use the shorthand arima(p,D,q) syntax to specify the default ARIMA(p, D, q) model,
% {\Delta ^D}{y_t} = c + {\phi _1}{\Delta ^D}{y_{t - 1}} +  \ldots  + {\phi _p}{\Delta ^D}{y_{t - p}} + {\varepsilon _t} + {\theta _1}{\varepsilon _{t - 1}} +  \ldots  + {\theta _q}{\varepsilon _{t - q}},
% where {\Delta ^D}{y_t} is a D^{th} differenced time series. You can write this model in condensed form using lag operator notation:
% \phi (L){(1 - L)^D}{y_t} = c + \theta (L){\varepsilon _t}.
% By default, all parameters in the created model object have unknown values, and the innovation distribution is Gaussian with constant variance.
% Specify the default ARIMA(1,1,1) model:

Mdl = arima(1,1,1)

% The output shows that the created model object, Mdl, has NaN values for all model parameters: the constant term, the AR and MA coefficients, and the variance. You can modify the created model using dot notation, or input it (along with data) to estimate.
% The property P has value 2 (p + D). This is the number of presample observations needed to initialize the AR model.
% Copyright 2015 The MathWorks, Inc.