# AIRLINE_FORECI - Forecasting Airline Model's Confidence Interval

Returns the confidence interval limits of the conditional mean forecast.

## Syntax

AIRLINE_FORECI(X, Order, mean, sigma, s, theta, theta2, T, alpha, upper)
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 first-lagged innovation (see model description).
theta2
is the coefficient of s-lagged innovation (see model description).
T
is the forecast time/horizon (expressed in terms of steps beyond end of the time series).
alpha
is the statistical significance level. If missing, a default of 5% is assumed.
upper
If true, returns the upper confidence interval limit. Otherwise, returns the lower limit.
upper description
0 return lower limit
1 return upper limit

## Remarks

1. The underlying model is described here.
2. Warning: AIRLINE_FORECI() function is deprecated as of version 1.63: use AIRLINE_FORE function instead.

3. The time series is homogeneous or equally spaced.
4. The time series may include missing values (e.g. #N/A) at either end.

## Examples

Example 1:

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A B C D
Date Data
1/1/2008 -0.300 AIRLINE
1/2/2008 -1.278 Mean 0.0481
1/3/2008 0.244 theta(1) 0.14
1/4/2008 1.276 theta(2) 0.30
1/6/2008 1.733 Sigma 2.74127
1/7/2008 -2.184 s 2
1/8/2008 -0.234
1/9/2008 1.095
1/10/2008 -1.087
1/11/2008 -0.690
1/12/2008 -1.690
1/13/2008 -1.847
1/14/2008 -0.978
1/15/2008 -0.774

Formula Description (Result)
=AIRLINE_AIC(Sheet1!\$B\$2:\$B\$15,1,\$D\$3,\$D\$6,\$D\$7,\$D\$4,\$D\$5) 65.6 Akaike's information criterion (AIC)
=AIRLINE_LLF(Sheet1!\$B\$2:\$B\$15,1,\$D\$3,\$D\$6,\$D\$7,\$D\$4,\$D\$5) -25.47 Log-Likelihood Function
=AIRLINE_CHECK(\$D\$3,\$D\$6,\$D\$7,\$D\$4,\$D\$5) 1 Is the AIRLINE model stable?