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

## Syntax

**EGARCH_AIC**(**X**, Order, **Mean**, **Alphas**, **Gammas**, **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 E-GARCH model mean (i.e., mu).
**Alphas**- are the parameters of the ARCH(p) component model (starting with the lowest lag).
**Gammas**- are the leverage parameters (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).
Value Innovation 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

- 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.
- EGARCH(p,q) model has 2p+q+2 estimated parameters.
- The number of gamma-coefficients must match the number of alpha-coefficients.
- 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.

## 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.

## Comments

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