Calculates the model's long-run average volatility.
Syntax
GARCHM_VL(alphas, betas)
- 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).
Remarks
- The underlying model is described here.
- The GARCH-M long-run average variance is defined as:
$$V_L=\frac{\alpha_o}{1-\sum_{i=1}^p\alpha_i-\sum_{j=1}^q\beta_j}$$ - The long-run variance is not affected by our choice of shock/innovation distribution.
- The time series is homogeneous or equally spaced.
- 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_VL($B$4:$B$5,$B$6) | The model long-run average volatility (0.999) |
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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