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)).

mean is the GARCH model mean (i.e. mu).

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 function of the innovations/residuals (1=Gaussian (default), 2=t-Distribution, 3=GED).

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

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 number of parameters in the input argument - alpha - determines the order of the ARCH component model.
7. The number of parameters in the input argument - beta - determines the order of the GARCH component model.
8. GARCH(p,q) model has p+q+2 parameters to estimate.
9. The AIC for a GARCH model is defined as:
   
   $AIC = 2(p+q+1) - 2\times \ln L^*$
   
   Where:
   
   • $\ln L^*$ is the log-likelihood function.
   • $T$ is the number of non-missing values.
   • $p$ is the order of the ARCH component model.
   • $q$ is the order of the GARCH component model.

Example 1:

Files Examples

Related Links

• Wikipedia - Akaike's Information Criterion (AIC)
• Wikipedia - Autoregressive conditional heteroskedasticity

References

• Hamilton, J .D.; Time Series Analysis , Princeton University Press (1994), ISBN 0-691-04289-6
• Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740