%% Specify a GARCH(1,1) Model
% As another illustration, consider specifying the GARCH(1,1) model
% y_t = \varepsilon_t,
% where
% \begin{array}{rcl} \varepsilon_t &=& \sigma_tz_t
% \\ \sigma^2_t &=&
% \kappa+\gamma_1\sigma^2_{t-1}+\alpha_1\varepsilon_{t-1}^2\end{array}
% Assume z_t follows a standard normal distribution.
% This model has one GARCH coefficient (corresponding to the lagged variance term) and one ARCH coefficient (corresponding to the lagged squared innovation term), both with unknown values. To specify this model, enter:

Mdl = garch('GARCH',NaN,'ARCH',NaN)

%
% The default value for the constant term is also NaN. Parameters with NaN values need to be estimated or otherwise specified before you can forecast or simulate the model. There is also a shorthand syntax to create a default GARCH(1,1) model:

Mdl = garch(1,1)

% The shorthand syntax returns a GARCH model with one GARCH coefficient and one ARCH coefficient, with default NaN values.
% Copyright 2015 The MathWorks, Inc.