GARCHM_AIC - Akaike's information criterion (AIC) for GARCH-M

Calculates the Akaike's information criterion (AIC) of a given estimated GARCH-M model (with corrections for small sample sizes).

Syntax

GARCHM_AIC(X, Order, mean, lambda, alphas, betas, innovation, v)

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 GARCH-M 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=t-Distribution, 3=GED).

value Description
1 Gaussian or Normal Distribution (default)
2 Student's t-Distribution
3 Generalized Error Distribution (GED)

v is the shape parameter (or degrees of freedom) of the innovations/residuals probability distribution function.

Remarks

  1. The underlying model is described here.
  2. Akaike's Information Criterion (AIC) is described here.
  3. The time series is homogeneous or equally spaced.
  4. The time series may include missing values (e.g. #N/A) at either end.
  5. Given a fixed data set, several competing models may be ranked according to their AIC, the model with the lowest AIC being the best.
  6. The GARCH-M(p,q) model with Gaussian has p+q+3 estimated parameters.
  7. The number of parameters in the input argument - alpha - determines the order of the ARCH component model.
  8. The number of parameters in the input argument - beta - determines the order of the GARCH component model.

Examples

Example 1:

 
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A B C D
Date Data    
January 10, 2008 -2.827 GARCH-M(1,1)  
January 11, 2008 -0.947 Mean -0.076
January 12, 2008 -0.877 Lambda 0.145
January 14, 2008 1.209 Alpha_0 0.593
January 13, 2008 -1.669 Alpha_1 0.000
January 15, 2008 0.835 Beta_1 0.403
January 16, 2008 -0.266    
January 17, 2008 1.361    
January 18, 2008 -0.343    
January 19, 2008 0.475    
January 20, 2008 -1.153    
January 21, 2008 1.144    
January 22, 2008 -1.070    
January 23, 2008 -1.491    
January 24, 2008 0.686    
January 25, 2008 0.975    
January 26, 2008 -1.316    
January 27, 2008 0.125    
January 28, 2008 0.712    
January 29, 2008 -1.530    
January 30, 2008 0.918    
January 31, 2008 0.365    
February 1, 2008 -0.997    
February 2, 2008 -0.360    
February 3, 2008 1.347    
February 4, 2008 -1.339    
February 5, 2008 0.481    
February 6, 2008 -1.270    
February 7, 2008 1.710    
February 8, 2008 -0.125    
February 9, 2008 -0.940    


  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$7,2,5) Akaike's information criterion (AIC) FOR t-Distribution with freedom = 5 (104.245)
  =GARCHM_AIC($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$7) Log-Likelihood Function (-45.482)
  =GARCHM_CHECK($D$3,$D$4,$D$5:$D$6,$D$7) The GARCH-M(1,1) model is stable? (1)

Files Examples

References

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