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

## Syntax

**AIRLINE_FORE** (**[x]**, order, µ, **σ**, **s**, θ, θ_{s}, **t**, return, α)

**[X]**- Required. Is the univariate time series data (a one-dimensional array of cells (e.g., rows or columns)).
**Order**- Optional. Is the time order in the data series (i.e., the first data point's corresponding date (earliest date = 1 (default), latest date = 0)).
Value Order 1 Ascending (the first data point corresponds to the earliest date) ( **default**).0 Descending (the first data point corresponds to the latest date). **µ**- Optional. Is the model mean (i.e., mu) or the long run mean of the differenced time series.
**σ**- Required. Is the standard deviation of the model's residuals/innovations.
**S**- Required. Is the length of seasonality (expressed in terms of lags, where s 1).
**θ**- Optional. Is the coefficient of the non-seasonal MA component (see model description).
**θ**_{s}- Optional. Is the coefficient of the seasonal MA component (see model description).
**T**- Required. Is the forecast time/horizon (expressed in terms of steps beyond the end of the time series).
**Return**- Optional. Is an integer switch to select the forecast output type: (1 = Mean (default), 2 = Std. Error, 3 = Term Struct, 4 = LL, 5 = UL).
Value Return 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. **α**- Optional. Is the statistical significance level (i.e., alpha). If missing or omitted, an alpha value 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 µ can take any value or be omitted, in which case a zero value is assumed.
- The value of the residuals/innovations’ standard deviation σ must be positive.
- The season length must be greater than one.
- The input argument for the non-seasonal MA parameter θ is optional and can be omitted, in which case no non-seasonal MA component is included.
- The input argument for the seasonal MA parameter θ
_{s}is optional and can be omitted, in which case no seasonal MA component is included.

## Files Examples

## Related Links

## References

- James Douglas Hamilton; Time Series Analysis, Princeton University Press; 1st edition(Jan 11, 1994), ISBN: 691042896.
- Tsay, Ruey S.; Analysis of Financial Time Series, John Wiley & SONS; 2nd edition(Aug 30, 2005), ISBN: 0-471-690740.

## Comments

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