# 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)).
Order Description
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.
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 conditonal 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.

## Examples

Example 1:

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A B C D E
Date Data GARCHM_MEAN
January 10, 2008 -2.827 0.068 GARCH(1,1)
January 11, 2008 -0.947 0.068 Mean -0.076
January 12, 2008 -0.877 0.068 Lambda 0.145
January 13, 2008 1.209 0.068 Alpha_0 0.593
January 14, 2008 -1.669 0.068 Alpha_1 0.000
January 15, 2008 0.835 0.068 Beta_1 0.403
January 16, 2008 -0.266 0.068
January 17, 2008 1.361 0.068
January 18, 2008 -0.343 0.068
January 19, 2008 0.475 0.068
January 20, 2008 -1.153 0.068
January 21, 2008 1.144 0.068
January 22, 2008 -1.070 0.068
January 23, 2008 -1.491 0.068
January 24, 2008 0.686 0.068
January 25, 2008 0.975 0.068
January 26, 2008 -1.316 0.068
January 27, 2008 0.125 0.068
January 28, 2008 0.712 0.068
January 29, 2008 -1.530 0.068
January 30, 2008 0.918 0.068
January 31, 2008 0.365 0.068
February 1, 2008 -0.997 0.068
February 2, 2008 -0.360 0.068
February 3, 2008 1.347 0.068
February 4, 2008 -1.339 0.068
February 5, 2008 0.481 0.068
February 6, 2008 -1.270 0.068
February 7, 2008 1.710 0.068
February 8, 2008 -0.125 0.068
February 9, 2008 -0.940 0.068

## References

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