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).

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.

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