Airline Model

The airline model is a special, but often used, case of multiplicative SARIMA model.

1. For a given seasonality length (s), the airline model is defined by four(4) parameters: \(\mu\),\(\sigma\),\(\theta\) and \(\Theta\). \[(1-L^s)(1-L)Y_t = \mu + (1-\theta L)(1-\Theta L^s)a_t\] OR \[ Z_t = (1-L^s)(1-L)Y_t = \mu + (1-\theta L)(1-\Theta L^s)a_t \] OR \[ Z_t = \mu -\theta \times a_{t-1}-\Theta \times a_{t-s} +\theta\times\Theta \times a_{t-s-1}+ a_t \] Where:
   • \(s\) is the length of seasonality.
   • \(\mu\) is the model mean
   • \(\theta\) is coefficient of first lagged innovation
   • \(\Theta\) is the coefficient of s-lagged innovation.
   • \(\left [a_t\right ] \) is the innovations time series.

Remarks

1. \(\left[Y_t\right]\) is not a stationary process, but the differenced time series \(\left[Y_t\right]\) is.
2. After we difference \(Y_t\) (i.e. \(Z_t\), the airline model is simplified to a special MA(s) model
3. The airline model has 5 parameters: \(\mu\,,\sigma\,,s\,,\theta\,,\Theta\)

Requirements

Header	SFSDK.H
Library	SFSDK.LIB
DLL	SFSDK.DLL