Calculates the Akaike's information criterion (AIC) of a given estimated GARCHM model (with corrections for small sample sizes).
Syntax
X is the univariate time series data (a 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 GARCHM model mean (i.e. mu).
lambda is the volatility coefficient for the mean. In finance, lambda is referenced as the risk premium.
alphas are the parameters of the ARCH(p) component model (starting with the lowest lag).
betas are the parameters of the GARCH(q) component model (starting with the lowest lag).
innovation is the probability distribution model for the innovations/residuals (1=Gaussian (default), 2=tDistribution, 3=GED).
value  Description 

1  Gaussian or Normal Distribution (default) 
2  Student's tDistribution 
3  Generalized Error Distribution (GED) 
v is the shape parameter (or degrees of freedom) of the innovations/residuals probability distribution function.
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.
 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 GARCHM(p,q) model with Gaussian has p+q+3 estimated parameters.
 The number of parameters in the input argument  alpha  determines the order of the ARCH component model.
 The number of parameters in the input argument  beta  determines the order of the GARCH component model.
Examples
Example 1:


Formula  Description (Result)  

=GARCHM_AIC($B$2:$B$32,1,$D$3,$D$4,$D$5:$D$6,$D$7)  Akaike's information criterion (AIC) FOR Guassian Distribution (96.964)  
=GARCHM_AIC($B$2:$B$32,1,$D$3,$D$4,$D$5:$D$6,$D$7,2,5)  Akaike's information criterion (AIC) FOR tDistribution with freedom = 5 (104.245)  
=GARCHM_AIC($B$2:$B$32,1,$D$3,$D$4,$D$5:$D$6,$D$7,3,4)  Akaike's information criterion (AIC) FOR GED with freedom = 4 (90.230)  
=GARCHM_LLF($B$2:$B$32,1,$D$3,$D$4,$D$5:$D$6,$D$7)  LogLikelihood Function (45.482)  
=GARCHM_CHECK($D$3,$D$4,$D$5:$D$6,$D$7)  The GARCHM(1,1) model is 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
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