GARCH Toolbox

Regression in a Monte Carlo Framework

In the general case, the functions garchsim, garchinfer, and garchpred process multiple realizations (i.e., sample paths) of univariate time series. That is, the outputs of garchsim, as well as the observed return series input to garchpred and garchinfer, can be matrices in which each column represents an independent realization. garchfit is different, in that the input observed return series of interest must be a vector (i.e., a single realization).

When simulating, inferring, and forecasting multiple realizations, the appropriate toolbox function applies a given regression matrix X to each realization of a univariate time series. For example, in the following command, garchsim applies a given X matrix to all 10 columns of the output series {_t}, {_t}, and {y_t}.

• [e,s,y] = garchsim(spec, 100, 10, [], X);
  

In a true Monte Carlo simulation of the above process, including a regression component, you would call garchsim inside a loop 10 times, once for each path. Each iteration would pass in a unique realization of X and produce single-column outputs.

Forecasting Using a Regression Component

Model Selection and Analysis