GARCHM_VL - Long-Run Volatility of the GARCH-M Model

Calculates the model's long-run average volatility.

Syntax

GARCHM_VL ([α], [β])

[α]

Required. Are the parameters of the ARCH(p) component model: [αo α1, α2 … αp] (starting with the lowest lag).

[β]

Optional. Are the parameters of the GARCH(q) component model: [β1, β2 … βq] (starting with the lowest lag).

Remarks

1. The underlying model is described here.
2. The time series is homogeneous or equally spaced.
3. The GARCH-M long-run average variance is defined as:$$V_L=\frac{\alpha_o}{1-\sum_{i=1}^p\alpha_i-\sum_{j=1}^q\beta_j}$$
4. The long-run variance is not affected by our choice of shock/innovation distribution.
5. The number of parameters in the input argument - [α_o α_1, α₂ … α_p] - determines the order of the ARCH component model.
6. The number of parameters in the input argument - [β_1, β₂ … β_q] - determines the order of the GARCH component model.

Files Examples

Related Links

• Wikipedia - Autoregressive conditional heteroskedasticity.

References

• James Douglas Hamilton; Time Series Analysis, Princeton University Press; 1st edition(Jan 11, 1994), ISBN: 691042896.
• Tsay, Ruey S.; Analysis of Financial Time Series, John Wiley & SONS; 2nd edition(Aug 30, 2005), ISBN: 0-471-690740.