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# ARMAX_SIM

Calculates the out-of-sample simulated values.

## Syntax

**ARMAX_SIM**(

**Y**,

**X**,

**Order**,

**Beta**,

**mean**,

**sigma**,

**phi**,

**theta**,

**T**,

**seed**)

**Y**

is the response or the dependent variable time series data array (one dimensional array of cells (e.g. rows or columns)).

**X**

is the independent variables (exogenous factors) time series data matrix, such that each column represents one variable.

**Order**

is the time order in the data series (i.e. the first data point's corresponding date (earliest date=1 (default), latest date=0)).

Order | Description |
---|---|

1 | ascending (the first data point corresponds to the earliest date) (default) |

0 | descending (the first data point corresponds to the latest date) |

**Beta**

are the coefficients array of the exogenous factors.

**mean**

is the ARMA long-run mean (i.e. mu).

**sigma**

is the standard deviation of the model's residuals.

**phi**

are the parameters of the AR(p) component model (starting with the lowest lag^{i}).

**theta**

are the parameters of the MA(q) component model (starting with the lowest lag).

**T**

is the simulation time/horizon (expressed in terms of steps beyond end of the time series).

**seed**

is an unsigned integer for setting up the random number generator(s)

## Remarks

- The underlying model is described here.
- The Log-Likelihood Function (LLF
^{i}) is described here. - ARMAX_SIM returns an array of one simulation path starting from the end of the input data.
- The response input data argument (i.e. latest observations) is optional. If ommitted, an array of zeroes is assumed.
- The number of observations in the factors (exogneous variables) input data must be greater than or equal to the size of response input data plus horizon.
- The time series (response and factors) are homogeneous or equally spaced.
- The time series may include missing values (e.g. #N/A) at either end.
- The observation at any given time is examined using the response and factors value, so a missing values (e.g. #N/A) in any of the input time series, deem the whole observation as missing.
- The long-run mean can take any value or ommitted, in which case a zero value is assumed.
- The residuals/innovations standard deviation (sigma) must greater than zero.
- For the input argument - phi:
- The input argument is optional and can be ommitted, in which case no AR component is included.
- The order of the parameters starts with the lowest lag
- One or more parameters may have missing value or an error code(i.e. #NUM!, #VALUE!, etc.).
- The order of the AR component model is solely determined by the order of the last value in the array with a numeric value (vs. missing, or error).

- For the input argument - theta:
- The input argument is optional and can be ommitted, in which case no MA component is included.
- The order of the parameters starts with the lowest lag
- One or more values in the input argument can be missing or an error code(i.e. #NUM!, #VALUE!, etc.).
- The order of the MA component model is solely determined by the order of the last value in the array with a numeric value (vs. missing, or error).

- The function ARMAX_SIM is available starting with version 1.63 SHAMROCK.

## Files Examples

## References

- Hamilton, J .D.; Time Series Analysis , Princeton University Press (1994), ISBN 0-691-04289-6
- Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740