# 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:

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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)