EGARCH - Defining an EGARCH Model

Returns a unique string to designate the specified EGARCH model.

Syntax

EGARCH (µ, [α], [γ], [β], f, ν)

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. The long-run mean can take any value or be omitted, in which case a zero value is assumed.
3. For the input argument - ([α]) (parameters of the ARCH component):
• The input argument is not optional.
• The value in the first element must be positive.
• The order of the parameters starts with the lowest lag.
• One or more parameters may have missing values or error codes (i.e., #NUM!, #VALUE!, etc.).
• In the case where alpha has one non-missing entry/element (first), no ARCH component is included.
• The order of the ARCH component model is solely determined by the order (minus one) of the last value in the array with a numeric value (vs. missing or error).
4. For the input argument - ([β]) (parameters of the GARCH component):
• The input argument is optional and can be omitted, in which case no GARCH component is included.
• The order of the parameters starts with the lowest lag.
• One or more parameters may have missing values or error codes (i.e., #NUM!, #VALUE!, etc.).
• The order of the GARCH component model is solely determined by the order of the last value in the array with a numeric value (vs. missing or error).
5. For the input argument - ([γ]) (leverage parameters):
• The input argument is not optional and can be omitted.
• The number of entries must match the number of alpha-coefficients (minus one).
• The order of the parameters starts with the lowest lag.
• One or more parameters may have missing values or error codes (i.e., #NUM!, #VALUE!, etc.). In essence, we may designate leverage for certain terms in the ARCH component model.
6. The number of gamma coefficients must match the number of alpha coefficients (minus one).
7. The shape parameter (ν) is only used for non-Gaussian distributions and is otherwise ignored.
8. For the student's t-distribution, the shape parameter’s value must be greater than four.

For GED distribution, the shape parameter’s value must be greater than one.

Files Examples

Related Links

• 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.