GARCHM_MEAN - GARCH-M Model Fitted Values

Returns an array of the fitted (in-sample) conditional mean values.

Syntax

GARCHM_MEAN(X, Order, Mean, Lambda, Alphas, Betas)

X

is the univariate time series data (a one-dimensional array of cells (e.g., rows or columns)).

Order

is the time order in the data series (i.e., the first data point's corresponding date (earliest date = 1 (default), latest date = 0)).

Value	Order
1	Ascending (the first data point corresponds to the earliest date) (default).
0	Descending (the first data point corresponds to the latest date).

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. If missing, a default of 0 is assumed.

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).

Remarks

1. The underlying model is described here.
2. The time series is homogeneous or equally spaced.
3. The time series may include missing values (e.g., #N/A) at either end.
4. The fitted conditional mean is calculated as: $$\hat x_t = \mu + \lambda \sigma_t$$ Where:
   • $\hat x_t$ is the fitted conditional mean at time $t$.
   • $\sigma_t$ is the fitted conditional volatility at time $t$.
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.

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.