Computes the goodness of fit measure (e.g. log-likelihood function (LLF), AIC, etc.) of the estimated Airline model.
Syntax
AIRLINE_GOF(X, Order, mean, sigma, s, theta, theta2, Type)
- X
- is the univariate time series data (one dimensional array of cells (e.g. rows or columns)).
- Order
- is the time order in the data series (i.e. the first data point's corresponding date (earliest date=1 (default), latest date=0)).
Order Description 1 ascending (the first data point corresponds to the earliest date) (default) 0 descending (the first data point corresponds to the latest date) - mean
- is the model mean (i.e. mu).
- sigma
- is the standard deviation of the model's residuals/innovations.
- s
- is the length of seasonality (expressed in terms of lags, where s > 1).
- theta
- is the coefficient of non-seasonal MA component (see model description).
- theta2
- is the coefficient of seasonal MA component (see model description).
- Type
- is an integer switch to select the goodness of fitness measure: (1=LLF (default), 2=AIC, 3=BIC, 4=HQC)
Order Description 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 multiplicative seasonal ARIMA model and it assumes independent and normally distributed residuals with constant variance.
- The function was added in version 1.63 SHAMROCK.
Examples
Example 1:
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| Formula | Description (Result) | |
|---|---|---|
| =AIRLINE_AIC(Sheet1!$B$2:$B$15,1,$D$3,$D$6,$D$7,$D$4,$D$5) | 65.6 | Akaike's information criterion (AIC) |
| =AIRLINE_LLF(Sheet1!$B$2:$B$15,1,$D$3,$D$6,$D$7,$D$4,$D$5) | -25.47 | Log-Likelihood Function |
| =AIRLINE_CHECK($D$3,$D$6,$D$7,$D$4,$D$5) | 1 | Is the AIRLINE model stable? |
Files Examples
Related Links
References
- Hamilton, J .D.; Time Series Analysis , Princeton University Press (1994), ISBN 0-691-04289-6
- Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740
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