Documentation 
[Y,E] =
simulate(Mdl,numObs)
[Y,E,V]
= simulate(Mdl,numObs)
[Y,E,V] = simulate(Mdl,numObs,Name,Value)
[Y,E] = simulate(Mdl,numObs) simulates sample paths and innovations from the ARIMA model, Mdl. The responses can include the effects of seasonality.
[Y,E,V] = simulate(Mdl,numObs) additionally simulates conditional variances, V.
[Y,E,V] = simulate(Mdl,numObs,Name,Value) simulates sample paths with additional options specified by one or more Name,Value pair arguments.
Mdl 
ARIMA or ARIMAX model, specified as an arima model returned by arima or estimate. The properties of Mdl cannot contain NaNs. 
numObs 
Positive integer that indicates the number of observations (rows) to generate for each path of the outputs Y, E, and V. 
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.
Notes

[1] 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.
[2] Enders, W. Applied Econometric Time Series. Hoboken, NJ: John Wiley & Sons, 1995.
[3] Hamilton, J. D. Time Series Analysis. Princeton, NJ: Princeton University Press, 1994.