# AIRLINE_FORE - Forecasting for Airline Model

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

1. The underlying model is described here.
2. The time series is homogeneous or equally spaced.
3. The time series may include missing values (e.g. #N/A) at either end.
4. The long-run mean argument (mean) can take any value or be omitted, in which case a zero value is assumed.
5. The value of the residuals/innovations standard deviation (sigma) must be positive.
6. The season length must be greater than one.
7. 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.
8. The input argument for the seasonal MA parameter - theta2 - is optional and can be omitted, in which case no seasonal MA component is included.