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 (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 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 a multiplicative seasonal ARIMA model. The model assumes independent and normally distributed residuals with constant variance.
4. The AIRLINE_CHECK() function examines the MA coefficients: $\theta ,{\theta _s},\theta \times {\theta _s}$ for process stability.

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.