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

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

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

Examples

Example 1:

 1 2 3 4 5 6
A B
GARCHM(1,1)
Mean -0.076
Lambda 0.145
Alpha_0 0.593
Alpha_1 0.000
Beta_1 0.403

Formula Description (Result)
=GARCHM_VL($B$4:$B$5,$B$6) The model long-run average volatility (0.999)