Examines the model's parameters for stability constraints (e.g. stationary, positive variance, etc.).
Syntax
GARCHM_CHECK(mean, lambda, alphas, betas, innovation, v)
- mean
- is the GARCH-M model mean (i.e. mu).
- lambda
- is the volatility coefficient for the mean. In finance, lambda is referenced as the risk premium.
- 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.
Remarks
- The underlying model is described here.
- The time series is homogeneous or equally spaced.
- To ensure positive conditional variance and finite unconditional variance, the model's cofficient must meet the following:
- $\alpha_o \gt 0$
- $\alpha_i \geq 0$
- $\beta_i \geq 0$
- $\sum_{i=1}^{max(p,q}(\alpha_i+\beta_i) \lt 1$
- The number of parameters in the input argument - alpha - determines the order of the ARCH component model.
- The number of parameters in the input argument - beta - determines the order of the GARCH component model.
Examples
Example 1:
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| Formula | Description (Result) |
|---|---|
| =GARCHM_CHECK($B$2,$B$3,$B$4:$B$5,$B$6) | The model is stable? (1) |
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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