Phone: +1 (888) 4279486
+1 (312) 2573777
Contact Us
ARMA_AIC
Calculates the Akaike's information criterion (AIC^{i}) of the given estimated ARMA^{i} 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 of the data series (i.e. whether the first data point corresponds to the earliest or latest date (earliest date=1 (default), latest date=0)).
Order  Description 

1  ascending (the first data point corresponds to the earliest date) 
0  descending (the first data point corresponds to the latest date) 
mean
is the ARMA model mean (i.e. mu).
sigma
is the standard deviation of the model's residuals/innovations.
phi
are the parameters of the AR(p) component model (starting with the lowest lag^{i}).
theta
are the parameters of the MA(q) component model (starting with the lowest lag).
Remarks
 Warning: ARMA_AIC() function is deprecated as of version 1.63: use ARMA_GOF function instead.
 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 standard deviation (i.e. ) of the ARMA model's residuals should be greater than zero.
 Given a fixed data set, several competing models may be ranked according to their AIC, the model with the lowest AIC being the best.
 The ARMA model has p+q+2 parameters, and it has independent and normally distributed residuals with constant variance.

Maximizing for the loglikelihood function, the AICc function for an ARMA model becomes:
Where:
 is the number of nonmissing values in the time series.
 is the order of the AR component model.
 os the order of the MA component model.
 is the standard deviation of the residuals.
 The number of parameters in the input argument  phi  determines the order of the AR component.
 The number of parameters in the input argument  theta  determines the order of the MA component.
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($B$2:$B$15,1,$D$3,$D$4,$D$5,$D$6)  Akaike's Information Criterion (1046.59)  
=ARMA_LLF^{i}($B$2:$B$15,1,$D$3,$D$4,$D$5,$D$6)  LogLikelihood Function (519.095)  
=ARMA_CHECK($D$3,$D$4,$D$5,$D$6)  Is ARMA model stable? (1) 
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