# EGARCH - Defining an EGARCH Model

Returns a unique string to designate the specified EGARCH model.

## Syntax

EGARCH(mean, alphas, gammas, betas, innovation, v)

mean is the EGARCH 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 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. The long-run mean can take any value or be omitted, in which case a zero value is assumed.
3. For the input argument - alpha (parameters of the ARCH component):
• The input argument is not optional.
• The value in the first element can not be missing or zero.
• 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 - beta (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. The number of gamma-coefficients must match the number of alpha-coefficients (minus one).
6. For the input argument - gamma (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.
7. The shape parameter (i.e. nu) is only used for non-Gaussian distributions and is otherwise ignored.
8. For student's t-distribution, the value of the shape parameter must be greater than four.
9. For GED distribution, the value of the shape parameter must be greater than one.