# GARCHM_MEAN - GARCH-M Model Fitted Values

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

## Syntax

GARCHM_MEAN ([x], order, µ, λ, [α], [β])

[X]
Required. Is the univariate time series data (a one-dimensional array of cells (e.g., rows or columns)).
Order
Optional. 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).
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).

## 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 - [αo α1, α2 … αp] - determines the order of the ARCH component model.
6. The number of parameters in the input argument - [β1, β2 … βq] - determines the order of the GARCH component model.