Returns a unique string to designate the specified GARCH-M model.
Syntax
GARCHM(mean, lambda, alphas, betas, innovation, v)
- mean
- is the GARCH-M model mean (i.e. mu). If missing, a default value of 0 is assumed.
- lambda
- is the volatility coefficient for the mean (aka. the risk premium). If missing, a default value of 0.0 is assumed.
- alphas
- are the parameters of the ARCH(p) component model (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. If missing, a default value of 5.0 is assumed.
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 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).
- 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 lambda input argument is optional. If omitted, no risk-premium is included in the mean model component (i.e. plain GARCH).
- The shape parameter (i.e. nu) is only used for non-Gaussian distribution 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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