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

- The underlying model is described here.
- The Log-Likelihood Function (LLF) is described here.
- Akaike's Information Criterion (AIC) is described here.
- Bayesian (Schwartz) Information Criterion (BIC) is described here.
- Hannan-Quinn Information Criterion (HQC) is described here.
- The time series is homogeneous or equally spaced.
- The time series may include missing values (e.g., #N/A) at either end.
- The airline model with order $s$ has 4 parameters: $\mu\,,\sigma\,\,,\theta\,,\mathit{and}\, \Theta$.
- The Airline model is a special case of a multiplicative seasonal ARIMA model, and it assumes independent and normally distributed residuals with constant variance.
- The function was added in version 1.63 SHAMROCK.

## Files Examples

## Related Links

## 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.

## Comments

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