Calculates the Akaike's information criterion (AIC) of the given airline model (with correction to small sample sizes)
Syntax
AIRLINE_AIC(X, Order, mean, sigma, s, theta, theta2)
 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 firstlagged innovation (see model description).
 theta2
 is the coefficient of slagged innovation (see model description).
Warning
AIRLINE_AIC() function is deprecated as of version 1.63: use AIRLINE_GOF function instead.
Remarks
 The underlying model is described here.
 Akaike's Information Criterion (AIC) 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.
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
Related Links
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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