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AIRLINE_CHECK
Examines the model's parameters for stability constraints (e.g. stationary, etc.).
Syntax
AIRLINE_CHECK(mean, sigma, s, theta, theta2)
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).
Remarks
 The underlying model is described here.
 The standard deviation (i.e. ) of the ARMA^{i} model's residuals should be greater than zero.
 The Airline model is a special case of multiplicative seasonal ARMA model.
 The Airline model is a special case of multiplicative seasonal ARIMA^{i} model, and it assumes independent and normally distributed residuals with constant variance.
Examples
Example 1:
A  B  C  D  

1  Date  Data  
2  1/1/2008  0.300 
ARMA 

3  1/2/2008  1.278  Mean  0.00258 
4  1/3/2008  0.244  Sigma  0.14 
5  1/4/2008  1.276  Phi_1  0.236 
6  1/6/2008  1.733  Theta_1  5.60E05 
7  1/7/2008  2.184  
8  1/8/2008  0.234  
9  1/9/2008  1.095  
10  1/10/2008  1.087  
11  1/11/2008  0.690  
12  1/12/2008  1.690  
13  1/13/2008  1.847  
14  1/14/2008  0.978  
15  1/15/2008  0.774 
Formula  Description (Result)  

=ARMA_AIC^{i}($B$2:$B$15,1,$D$3,$D$4,$D$5,$D$6)  1046.59  Akaike's information criterion (AIC)  
=ARMA_LLF^{i}($B$2:$B$15,1,$D$3,$D$4,$D$5,$D$6)  519.095  LogLikelihood Function  
=ARMA_CHECK($D$3,$D$4,$D$5,$D$6)  1  Is ARMA 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