Forecast conditional variances from conditional variance models

`V = forecast(Mdl,numperiods,Y0)`

`V = forecast(Mdl,numperiods,Y0,Name,Value)`

generates forecasts with additional options specified by one or more name-value pair
arguments. For example, you can initialize the model by specifying presample
conditional variances.`V`

= forecast(`Mdl`

,`numperiods`

,`Y0`

,`Name,Value`

)

If the conditional variance model

`Mdl`

has an offset (`Mdl.Offset`

),`forecast`

subtracts it from the specified presample responses`Y0`

to obtain presample innovations`E0`

. Subsequently,`forecast`

uses`E0`

to initialize the conditional variance model for forecasting.`forecast`

sets the number of sample paths to forecast`numpaths`

to the maximum number of columns among the presample data sets`Y0`

and`V0`

. All presample data sets must have either`numpaths`

> 1 columns or one column. Otherwise,`forecast`

issues an error. For example, if`Y0`

has five columns, representing five paths, then`V0`

can either have five columns or one column. If`V0`

has one column, then`forecast`

applies`V0`

to each path.`NaN`

values in presample data sets indicate missing data.`forecast`

removes missing data from the presample data sets following this procedure:`forecast`

horizontally concatenates the specified presample data sets`Y0`

and`V0`

such that the latest observations occur simultaneously. The result can be a jagged array because the presample data sets can have a different number of rows. In this case,`forecast`

prepads variables with an appropriate amount of zeros to form a matrix.`forecast`

applies list-wise deletion to the combined presample matrix by removing all rows containing at least one`NaN`

.`forecast`

extracts the processed presample data sets from the result of step 2, and removes all prepadded zeros.

List-wise deletion reduces the sample size and can create irregular time series.

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