EGARCH_AIC - EGARCH Model's Akaike's Information Criterion (AIC)

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

Syntax

EGARCH_AIC ([x], order, µ, [α], [γ], [β], f, ν)

[X]

Required. Is the univariate time series data (a one-dimensional array of cells (e.g., rows or columns)).

Order

Optional. Is the time order in the data series (i.e., the first data point's corresponding date (earliest date = 1 (default), latest date = 0)).

Value	Order
1	Ascending (the first data point corresponds to the earliest date) (default).
0	Descending (the first data point corresponds to the latest date).

µ

Optional. Is the GARCH model long-run mean (i.e., mu). If missing, the process mean is assumed to be zero.

[α]

Required. Are the parameters of the ARCH(p) component model: [αo α1, α2 … αp] (starting with the lowest lag).

[γ]

Optional. Are the leverage parameters: [γ1, γ2 … γp] (starting with the lowest lag).

[β]

Optional. Are the parameters of the GARCH(q) component model: [β1, β2 … βq] (starting with the lowest lag).

F

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

Value	Probability Distribution
1	Gaussian or Normal Distribution (default).
2	Student's t-Distribution.
3	Generalized Error Distribution (GED).

ν

Optional. 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. EGARCH (p, q) model has 2p+q+2 estimated parameters.
7. The number of gamma coefficients must match the number of alpha coefficients (minus one).
8. The number of parameters in the input argument - [α_o α_1, α₂ … α_p] - determines the order of the ARCH component model.
9. The number of parameters in the input argument - [β_1, β₂ … β_q] - determines the order of the GARCH component model.

Files Examples

Related Links

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

References

• 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: 0-471-690740.