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.


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

Required. Is the univariate time series data (a one-dimensional array of cells (e.g., rows or columns)).
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).
Optional. Is the model mean (i.e., mu) or the long run mean of the differenced time series.
Required. Is the standard deviation of the model's residuals/innovations.
Required. Is the length of seasonality (expressed in terms of lags, where s 1).
Optional. Is the coefficient of the non-seasonal MA component (see model description).
Optional. Is the coefficient of the seasonal MA component (see model description).
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).


  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.

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