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V = simulate(model,numObs)
[V,Y] = simulate(model,numObs)
[V,Y] = simulate(model,numObs,Name,Value)
V = simulate(model,numObs) simulates sample paths of conditional variances from a GARCH process.
[V,Y] = simulate(model,numObs) additionally simulates sample response paths.
[V,Y] = simulate(model,numObs,Name,Value) simulates sample paths with additional options specified by one or more Name,Value pair arguments.
model 
garch model object, as created by garch or estimate. The input model object cannot have any NaN values. 
numObs 
Positive integer indicating the number of observations (rows) generated for each path of outputs V and Y. 
Specify optional commaseparated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.
'NumPaths' 
Positive integer indicating the number of sample paths (columns) generated for outputs V and Y. Default: 1 
Notes

V 
numObsbyNumPaths matrix of conditional variances of the mean zero innovations associated with Y. 
Y 
numObsbyNumPaths matrix of response data. Y usually represents a time series of innovations with mean zero and conditional variances are given in V (a continuation of the presample innovation series E0). Y might also represent a time series of innovations with mean zero plus an offset. The inclusion of an offset is signaled by a nonzero Offset property in model. If the input model includes an offset, the offset is added to the underlying meanzero innovations such that Y represents a time series of offsetadjusted innovations. 
[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] Hamilton, J. D. Time Series Analysis. Princeton, NJ: Princeton University Press, 1994.
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