Calculates the out-of-sample conditional mean and error forecast

## Syntax

**AIRLINE_FORE**(

**X**,

**Order**,

**mean**,

**sigma**,

**s**,

**theta**,

**theta2**,

**T**,

**Type**,

**alpha**)

- 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 the end of the time series).
- Type
- is an integer switch to select the forecast output type: (1=mean (default), 2=Std. Error, 3=Term Struct, 4=LL, 5=UL)
Order Description 1 Mean forecast value (default) 2 Forecast standard error (aka local volatility) 3 Volatility term structure 4 Lower limit of the forecast confidence interval. 5 Upper limit of the forecast confidence interval. - alpha
- is the statistical significance level. If missing, a default of 5% is assumed.

## Remarks

- The underlying model is described here.
- 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.

## 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

Article is closed for comments.