The airline model is a special, but often used, case of multiplicative ARIMA model. For a given seasonality length (s), the airline model is defined by four(4) parameters: $\mu$, $\sigma$, $\theta$, and $\Theta$).

Where:

- $s$ is the length of seasonality.
- $\mu$ is the model mean.
- $\theta$ is the coefficient of first lagged innovation.
- $\Theta$ is the coefficient of s-lagged innovation.
- $\left [a_t\right ]$ is the innovations time series.

## Remarks

- The AirLine model can be viewed as a "cascade" of two models:
- The first model is non-stationary: $$(1-L^s)(1-L)Y_t = Z_t$$
- The second model is wide-sense stationary: $$Z_t = \mu + (1-\theta L)(1-\Theta L^s)a_t$$

- The stationary component is a special form of the moving average model.
- The airline model of order ($s$) has 4 free parameters: $\mu\,,\sigma\,\,,\theta\,,\Theta$

## 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.

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