Calculates the out-of-sample simulated values.

## Syntax

**ARIMA_SIM**(

**X**, Order,

**d**,

**Mean**,

**Sigma**,

**Phi**,

**Theta**,

**T**,

**Seed**)

**X**- is the univariate time series data (a one-dimensional array of cells (e.g., rows or columns)).
**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). **d**- is the degree of the differencing (i.e., d).
**Mean**- is the ARMA model mean (i.e., mu).
**Sigma**- is the standard deviation of the model's residuals/innovations.
**Phi**- are the parameters of the AR(p) component model (starting with the lowest lag).
**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 the 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) is described here.
- ARMA_SIM returns an array of one simulation path starting from the end of the input data.
- The input data argument (i.e., latest observations) is optional. If omitted, an array of zeroes is assumed.
- The time series is homogeneous or equally spaced.
- The time series may include missing values (e.g., #N/A) at either end.
- For the input argument - phi:
- The input argument is optional and can be omitted, 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 values 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 omitted, 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 was added in version 1.63 SHAMROCK.

## Files Examples

## Related Links

## 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.

## Comments

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