Calculates the Akaike's information criterion (AIC) of the given estimated ARMA model (with the correction to small sample sizes).
Syntax
ARMA_AIC(X, Order, mean, sigma, phi, theta)
 X
 is the univariate time series data (a onedimensional 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 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).
 theta
 are the parameters of the MA(q) component model (starting with the lowest lag).
Warning
ARMA_AIC() function is deprecated as of version 1.63: use ARMA_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 ARMA model's residuals' standard deviation (i.e., $\sigma$) 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:
$$\mathit{AICc}(p,q)= \ln(\hat\sigma^2(p,q))+\frac{2\times(p+q)}{T}$$
Where:
 $T$ is the number of nonmissing values in the time series.
 $p$ is the order of the AR component model.
 $q$ is the order of the MA component model.
 $\hat\sigma$ 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:


Formula  Description (Result) 

=ARMA_AIC($B$2:$B$15,1,$D$3,$D$4,$D$5,$D$6)  Akaike's Information Criterion (1046.59) 
=ARMA_LLF($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 the ARMA model stable? (1) 
Files Examples
Related Links
References
 D. S.G. Pollock; Handbook of Time Series Analysis, Signal Processing, and Dynamics; Academic Press; Har/Cdr edition(Nov 17, 1999), ISBN: 125609906
 James Douglas Hamilton; Time Series Analysis; Princeton University Press; 1st edition(Jan 11, 1994), ISBN: 691042896
 Tsay, Ruey S.; Analysis of Financial Time Series; John Wiley & SONS; 2nd edition(Aug 30, 2005), ISBN: 0471690740
 Box, Jenkins, and Reisel; Time Series Analysis: Forecasting and Control; John Wiley & SONS.; 4th edition(Jun 30, 2008), ISBN: 470272848
 Walter Enders; Applied Econometric Time Series; Wiley; 4th edition(Nov 03, 2014), ISBN: 1118808568
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