simulate
Monte Carlo simulation of ARIMA or ARIMAX models
Syntax
[Y,E] =
simulate(Mdl,numObs)
[Y,E,V]
= simulate(Mdl,numObs)
[Y,E,V] = simulate(Mdl,numObs,Name,Value)
Description
[
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.
Input 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 
NameValue Arguments
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Namevalue arguments must appear after other arguments, but the order of the
pairs does not matter.
Before R2021a, use commas to separate each name and value, and enclose
Name
in quotes.

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, andsimulate
removes them. The software merges the presample data, then uses listwise deletion to remove anyNaN
s in the presample data matrix orX
. That is,simulate
setsPreSample
=[Y0 E0 V0]
, then it removes any row inPreSample
orX
that contains at least oneNaN
.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.
Output Arguments






Examples
References
[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.
See Also
Objects
Functions
Topics
 Simulate Stationary Processes
 Simulate TrendStationary and DifferenceStationary Processes
 Simulate Multiplicative ARIMA Models
 Simulate Conditional Mean and Variance Models
 Monte Carlo Simulation of Conditional Mean Models
 Presample Data for Conditional Mean Model Simulation
 Transient Effects in Conditional Mean Model Simulations
 Monte Carlo Forecasting of Conditional Mean Models