mean is the GARCH-M model mean (i.e. mu).

lambda is the volatility coefficient for the mean. In finance, lambda is referenced as the risk premium.

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 model for the innovations/residuals (1=Gaussian (default), 2=t-Distribution, 3=GED).

v 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 cofficient must meet the following:
   • $\alpha_o \gt 0$
   • $\alpha_i \geq 0$
   • $\beta_i \geq 0$
   • $\sum_{i=1}^{max(p,q}(\alpha_i+\beta_i) \lt 1$
4. The number of parameters in the input argument - alpha - determines the order of the ARCH component model.
5. The number of parameters in the input argument - beta - determines the order of the GARCH component model.

Example 1:

Files Examples

Related Links

• Wikipedia - Autoregressive conditional heteroskedasticity

References

• Hamilton, J .D.; Time Series Analysis , Princeton University Press (1994), ISBN 0-691-04289-6
• Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740