Calculates the out-of-sample conditional simulated values

## Syntax

**AIRLINE_SIM**(

**X**,

**Order**,

**mean**,

**sigma**,

**s**,

**theta**,

**theta2**,

**T**,

**seed**)

**X** is the univariate time series data (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) |

**mean** is the model mean (i.e. mu).

**sigma** is the standard deviation of the model's residuals/innovations.

**s** is the length of seasonality (expressed in terms of lags, where s > 1).

**theta** is the coefficient of non-seasonal MA component (see model description).

**theta2** is the coefficient of seasonal MA component (see model description).

**T** is the forecast 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.
- 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 ommitted, 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.
- The long-run mean argument (mean) can take any value or be omitted, in which case a zero value is assumed.
- The value of the residuals/innovations standard deviation (sigma) must be positive.
- The season length must be greater than one.
- The input argument for the non-seasonal MA parameter - theta - is optional and can be omitted, in which case no non-seasonal MA component is included.
- The input argument for the seasonal MA parameter - theta2 - is optional and can be omitted, in which case no seasonal MA component is included.
- 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

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