Computes the goodness of fit measure (e.g. loglikelihood function (LLF), AIC, etc.) of the estimated Airline model.
Syntax
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 nonseasonal 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  LogLikelihood Function (LLF) (default) 
2  Akaike Information Criterion (AIC) 
3  Schwarz/Bayesian Information Criterion (SIC/BIC) 
4  HannanQuinn information criterion (HQC) 
Remarks
 The underlying model is described here.
 The LogLikelihood Function (LLF) is described here.
 Akaike's Information Criterion (AIC) is described here.
 Bayesian (Schwartz) Information Criterion (BIC) is described here.
 "HannanQuinn 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:


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$5)  25.47  LogLikelihood Function  
=AIRLINE_CHECK($D$3,$D$6,$D$7,$D$4,$D$5)  1  Is the AIRLINE model stable? 
Files Examples
References
 Hamilton, J .D.; Time Series Analysis , Princeton University Press (1994), ISBN 0691042896
 Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0471690740
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