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
- The underlying model is described here.
- The long-run mean can take any value or be omitted, in which case a zero value is assumed.
- 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).
- 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).
- The number of gamma-coefficients must match the number of alpha-coefficients (minus one).
- 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.
- The shape parameter (i.e. nu) is only used for non-Gaussian distributions and is otherwise ignored.
- For student's t-distribution, the value of the shape parameter must be greater than four.
- For GED distribution, the value of the shape parameter must be greater than one.
Files Examples
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
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