# forecast

Forecast conditional variances from conditional variance models

## Description

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`

)

## Examples

## Input Arguments

## Output Arguments

## More About

## Algorithms

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.

## References

[1] Bollerslev, T. “Generalized Autoregressive Conditional
Heteroskedasticity.” *Journal of Econometrics*. Vol. 31,
1986, pp. 307–327.

[2] Bollerslev, T. “A Conditionally Heteroskedastic Time Series Model for
Speculative Prices and Rates of Return.” *The Review of Economics and
Statistics*. Vol. 69, 1987, pp. 542–547.

[3] Box, G. E. P., G. M. Jenkins, and G. C. Reinsel. *Time Series
Analysis: Forecasting and Control*. 3rd ed. Englewood Cliffs, NJ:
Prentice Hall, 1994.

[4] Enders, W. *Applied Econometric Time Series*. Hoboken, NJ:
John Wiley & Sons, 1995.

[5] Engle, R. F. “Autoregressive Conditional Heteroskedasticity with
Estimates of the Variance of United Kingdom Inflation.”
*Econometrica*. Vol. 50, 1982, pp. 987–1007.

[6] Glosten, L. R., R. Jagannathan, and D. E. Runkle. “On
the Relation between the Expected Value and the Volatility of the Nominal Excess Return
on Stocks.” *The Journal of Finance*. Vol. 48, No. 5, 1993,
pp. 1779–1801.

[7] Hamilton, J. D. *Time Series Analysis*. Princeton, NJ:
Princeton University Press, 1994.

[8] Nelson, D. B. “Conditional Heteroskedasticity in Asset Returns: A New
Approach.” *Econometrica*. Vol. 59, 1991, pp.
347–370.

## Version History

**Introduced in R2012a**