Regression in Monte Carlo
In the general case, these functions process multiple realizations
(that is, sample paths) of univariate time series:
The outputs of garchsim and
the observed return series input to garchpred and garchinfer can be time series matrices in
which each column represents an independent realization. garchfit is different, because the input
observed return series of interest must be a vector (that is, 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 {εt}, {σt},
and {yt}:
NumSamples = 100;
NumPaths = 10;
strm = RandStream('mt19937ar','Seed',22883);
RandStream.setDefaultStream(strm);
[e,s,y] = garchsim(spec,NumSamples,NumPaths,[],X);In
a true Monte Carlo simulation of this 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 a single-column
output.
 | Regression in Forecasting | | Ordinary Least Squares Regression |  |
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