GARCHM_CHECK - Check Parameters' Values for Model Stability

Mohamad

October 27, 2016 23:18

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

Syntax

GARCHM_CHECK (µ, λ, [α], [β], f, ν)

µ

Optional. Is the GARCH model long-run mean (i.e., mu). If missing, the process mean is assumed to be zero.

λ

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.

[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).

F

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).

ν

Optional. Is the shape parameter (or degrees of freedom) of the innovations/residuals’ probability distribution function.

The underlying model is described here.
The time series is homogeneous or equally spaced.
To ensure positive conditional variance and finite unconditional variance, the model's coefficient must meet the following:
- $\alpha_o \gt 0$.
- $\alpha_i \geq 0$.
- $\beta_i \geq 0$.
- $\sum_{i=1}^{max(p,q}(\alpha_i+\beta_i) \lt 1$.
The number of parameters in the input argument - [α_oα_1, α₂… α_p] - determines the order of the ARCH component model.
The number of parameters in the input argument - [β_1, β₂… β_q] - determines the order of the GARCH component model.

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.