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AIRLINE_GOF
Calculates the Akaike's information criterion (AIC^{i}) of the given airline model (with correction to small sample sizes)
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 seasoanl MA component (see model description).
Type
is an integer switch to select the goodness of fitness measure: (1=LLF^{i} (default), 2=AIC, 3=BIC^{i}, 4=HQC^{i})
Order  Description 

1  LogLikelihood Function (LLF) (default) 
2  Akaike Information Criterion (AIC) 
3  Schwarz/Bayesian Information Criterion (SIC^{i}/BIC^{i}) 
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 has 4 parameters:
 The Airline model is a special case of multiplicative seasonal ARIMA^{i} model, and it assumes independent and normally distributed residuals with constant variance.
 The function was added in version 1.63 SHAMROCK.
Examples
Example 1:
A  B  C  D  

1  Date  Data  
2  1/1/2008  0.300 
AIRLINE 

3  1/2/2008  1.278  Mean  0.0481 
4  1/3/2008  0.244  theta(1)  0.14 
5  1/4/2008  1.276  theta(2)  0.30 
6  1/6/2008  1.733  Sigma  2.74127 
7  1/7/2008  2.184  s  2 
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)  

=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