# GARCH_CHECK - Check parameters' values for model stability

Examines the model's parameters for stability constraints (e.g. stationary, positive variance, etc.).

## Syntax

GARCH_CHECK(mean, alphas, betas, innovation, v)

mean is the model mean (i.e. mu).

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 of the innovations/shocks (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 factor (or degrees of freedom) of the innovations/residuals probability distribution function.

## Remarks

1. The underlying model is described here.
2. The time series is homogeneous or equally spaced.
3. The number of parameters in the input argument - alpha - determines the order of the ARCH component model.
4. The number of parameters in the input argument - beta - determines the order of the GARCH component model.
5. To ensure positive conditional variance and finite unconditional variance, the model's cofficient must meet the following:
• $\alpha_o \gt 0$
• $\alpha_i \geq 0$
• $\beta_i \geq 0$

• $\sum_{i=1}^{max(p,q}(\alpha_i+\beta_i) \lt 1$

## Examples

Example 1:

 1 2 3 4 5
A B
GARCH(1,1)
Mean -0.160
Alpha_0 0.608
Alpha_1 0.000
Beta_1 0.391

Formula Description (Result)
=GARCH_CHECK($B$2,$B$3:$B$4,$B$5) The model is stable? (1)