AIRLINE_CHECK - Check parameters' values for model stability

 

Examines the model's parameters for stability constraints (e.g. stationary, invertibility, causality, 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 first-lagged innovation (see model description).

theta2 is the coefficient of s-lagged innovation (see model description).

 

Remarks

  1. The underlying model is described here.
  2. The standard deviation (i.e. $\sigma$) of the ARMA model's residuals should be greater than zero.
  3. The Airline model is a special case of multiplicative seasonal ARIMA model. The model assumes independent and normally distributed residuals with constant variance.
  4. The AIRLINE_CHECK examines the MA coefficients: $\theta, \Theta, \theta\times\Theta$ for process stability.

Examples

Example 1:

 
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A B C D
Date Data    
1/1/2008 -0.300 AIRLINE  
1/2/2008 -1.278 Mean 0.0481
1/3/2008 0.244 theta(1) 0.14
1/4/2008 1.276 theta(2) 0.30
1/6/2008 1.733 Sigma 2.74127
1/7/2008 -2.184 s 2
1/8/2008 -0.234    
1/9/2008 1.095    
1/10/2008 -1.087    
1/11/2008 -0.690    
1/12/2008 -1.690    
1/13/2008 -1.847    
1/14/2008 -0.978    
1/15/2008 -0.774    


  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

References

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