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# ARIMA_SIM

Calculates the out-of-sample simulated values.

## Syntax

**ARIMA**(

^{i}_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^{i} 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^{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. - 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

## 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