Monte Carlo simulation of ARIMA or ARIMAX models
[Y,E] =
simulate(Mdl,numObs)
[Y,E,V]
= simulate(Mdl,numObs)
[Y,E,V] = simulate(Mdl,numObs,Name,Value)
[
simulates sample paths and innovations from the ARIMA model, Y
,E
] =
simulate(Mdl
,numObs
)Mdl
. The responses can include the effects of seasonality.
[
additionally simulates conditional variances, Y
,E
,V
]
= simulate(Mdl
,numObs
)V
.
[Y,E,V] = simulate(Mdl,numObs,
simulates sample paths with additional options specified by one or more Name,Value
)Name,Value
pair arguments.

ARIMA or ARIMAX model, specified as an The properties of 

Positive integer that indicates the number of observations (rows) to generate for each path of the outputs 
Specify optional
commaseparated pairs of Name,Value
arguments. Name
is
the argument name and Value
is the corresponding value.
Name
must appear inside quotes. You can specify several name and value
pair arguments in any order as
Name1,Value1,...,NameN,ValueN
.

Mean zero presample innovations that provide initial values for the model. Default: 

Positive integer that indicates the number of sample paths (columns) to generate. Default: 

Positive presample conditional variances which provide initial values for any conditional variance model. If the variance of the model is constant, then Default: 

Matrix of predictor data with length Default: 

Presample response data that provides initial values for the model. Default: 
Notes
NaN
s indicate missing values, and simulate
removes them. The software merges the presample data, then uses listwise deletion to remove any NaN
s in the presample data matrix or X
. That is, simulate
sets PreSample
= [Y0 E0 V0]
, then it removes any row in PreSample
or X
that contains at least one NaN
.
The removal of NaN
s in the main data reduces the effective sample size. Such removal can also create irregular time series.
simulate
assumes that you synchronize the predictor series such that the most recent observations occur simultaneously. The software also assumes that you synchronize the presample series similarly.






[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.