GARCHM_CHECK - Check Parameters' Values for Model Stability

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


GARCHM_CHECK (µ, λ, [α], [β], f, ν)

Optional. Is the GARCH model long-run mean (i.e., mu). If missing, the process mean is assumed to be zero.
Optional. Is the volatility coefficient for the mean. In finance, lambda is referenced as the risk premium. If missing, a default of 0 is assumed.
Required. Are the parameters of the ARCH(p) component model: [αo α1, α2 … αp] (starting with the lowest lag).
Optional. Are the parameters of the GARCH(q) component model: [β1, β2 … βq] (starting with the lowest lag).
Optional. Is the probability distribution function of the innovations/residuals (1 = Gaussian (default), 2 = t-Distribution, 3 = GED).
Value Probability Distribution
1 Gaussian or Normal Distribution (default).
2 Student's t-Distribution.
3 Generalized Error Distribution (GED).
Optional. Is the shape parameter (or degrees of freedom) of the innovations/residuals’ probability distribution function.


  1. The underlying model is described here.
  2. The time series is homogeneous or equally spaced.
  3. To ensure positive conditional variance and finite unconditional variance, the model's coefficient must meet the following:
    • $\alpha_o \gt 0$.
    • $\alpha_i \geq 0$.
    • $\beta_i \geq 0$.
    • $\sum_{i=1}^{max(p,q}(\alpha_i+\beta_i) \lt 1$.
  4. The number of parameters in the input argument - [αo α1, α2 … αp] - determines the order of the ARCH component model.
  5. The number of parameters in the input argument - [β1, β2 … βq] - determines the order of the GARCH component model.

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