# AIRLINE_CHECK - Check parameters' values for model stability

Examines the model's parameters for stability constraints (e.g. stationary, invertibility, causality, etc.).

## Syntax

AIRLINE_CHECK(mean, sigma, s, theta, theta2)

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).

## Remarks

1. The underlying model is described here.
2. The standard deviation (i.e. $\sigma$) of the ARMA model's residuals should be greater than zero.
3. The Airline model is a special case of multiplicative seasonal ARIMA model. The model assumes independent and normally distributed residuals with constant variance.
4. The AIRLINE_CHECK examines the MA coefficients: $\theta, \Theta, \theta\times\Theta$ for process stability.

## Examples

Example 1:

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
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?

## References

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