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 responsesY0
to obtain presample innovationsE0
. Subsequently,forecast
usesE0
to initialize the conditional variance model for forecasting.forecast
sets the number of sample paths to forecastnumpaths
to the maximum number of columns among the presample data setsY0
andV0
. All presample data sets must have eithernumpaths
> 1 columns or one column. Otherwise,forecast
issues an error. For example, ifY0
has five columns, representing five paths, thenV0
can either have five columns or one column. IfV0
has one column, thenforecast
appliesV0
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 setsY0
andV0
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 oneNaN
.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.