Airline - Defining an Airline model

Returns a unique string to designate the specified Airline model.

Syntax

AIRLINE (µ, σ, s, θ, θ_s)

µ

Optional. Is the model mean (i.e., mu) or the long-run mean of the differenced time series.

σ

Required. Is the standard deviation of the model's residuals/innovations.

S

Required. Is the length of seasonality (expressed in terms of lags, where s > 1).

θ

Optional. Is the coefficient of the non-seasonal MA component (see model description).

θ_s

Optional. Is the coefficient of the seasonal MA component (see model description).

Remarks

1. The underlying model is described here.
2. The long-run mean argument (mean) can take any value or be omitted, in this case a zero value is assumed.
3. The value of the residuals/innovations standard deviation (sigma) must be positive.
4. The season length must be greater than one.
5. The input argument for the non-seasonal MA parameter - θ - is optional and can be omitted, in which case no non-seasonal MA component is included.
6. The input argument for the seasonal MA parameter - θ_s - is optional and can be omitted, in which case no seasonal MA component is included.
7. The function was added in version 1.63 SHAMROCK.

Files Examples

Related Links

• Wikipedia - Akaike's Information Criterion (AIC).
• Wikipedia - Autoregressive moving average model.

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.