AIRLINE_GOF - Goodness of Fit of an Airline Model

Computes the goodness of fit measure (e.g., log-likelihood function (LLF), AIC, etc.) of the estimated Airline model.

Syntax

AIRLINE_GOF ([x], order, µ, σ, s, θ, θ_s, return)

[X]

Required. Is the univariate time series data (a one-dimensional array of cells (e.g., rows or columns)).

Order

Optional. Is the time order in the data series (i.e., the first data point's corresponding date (earliest date = 1 (default), latest date = 0)).

Value	Order
1	Ascending (the first data point corresponds to the earliest date) (default).
0	Descending (the first data point corresponds to the latest date).

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).

Return

Optional. Is an integer switch to select the goodness of fitness measure: (1 = LLF (default), 2 = AIC, 3 = BIC, 4 = HQC).

Value	Return
1	Log-Likelihood Function (LLF) (default).
2	Akaike Information Criterion (AIC).
3	Schwarz/Bayesian Information Criterion (SIC/BIC).
4	Hannan-Quinn information criterion (HQC).

Remarks

1. The underlying model is described here.
2. The Log-Likelihood Function (LLF) is described here.
3. Akaike's Information Criterion (AIC) is described here.
4. Bayesian (Schwartz) Information Criterion (BIC) is described here.
5. Hannan-Quinn Information Criterion (HQC) is described here.
6. The time series is homogeneous or equally spaced.
7. The time series may include missing values (e.g., #N/A) at either end.
8. The airline model with order $s$ has 4 parameters: $\mu\,,\sigma\,\,,\theta\,,\mathit{and}\, \Theta$.
9. The Airline model is a special case of a multiplicative seasonal ARIMA model, and it assumes independent and normally distributed residuals with constant variance.
10. 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.