Returns an array for the fitted GARCH-M model standardized residuals.

## Syntax

**GARCHM_RESID** (**X**, Order, **Mean**, Lambda, **Alphas**, **Betas**, Innovation, ν)

**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).
**Innovation**- is the probability distribution function of the innovations/residuals (1 = Gaussian (default), 2 = t-Distribution, 3 = GED).
Value Innovation 1 Gaussian or Normal Distribution ( **default**).2 Student's t-Distribution. 3 Generalized Error Distribution (GED). **ν**- is the shape parameter (or degrees of freedom) of the innovations/residuals probability distribution function. If missing, a default of 5.0 is assumed.

## Remarks

- The underlying model is described here.
- The time series is homogeneous or equally spaced.
- The time series may include missing values (e.g., #N/A) at either end.
- The standardized residuals have a mean of zero and a variance of one (1).
- The GARCH-M model's standardized residuals is defined as: $$\epsilon_t = \frac{a_t}{\sigma_t}$$ $$a_t = x_t - \mu -\lambda \sigma_t$$ Where:
- $\epsilon$ is the GARCH-M model's standardized residual at time $t$.
- $a_t$ is the GARCH-M model's residual at time $t$.
- $x_t$ is the value of the time series at time $t$.
- $\mu$ is the GARCH-M mean.
- $\sigma_t$ is the GARCH-M conditional volatility at time $t$.
- $\lambda$ is the volatility coefficient in the conditional mean.

- The number of parameters in the input argument - alpha - determines the order of the ARCH component model.
- The number of parameters in the input argument - beta - determines the order of the GARCH component model.

## Files Examples

## Related Links

## 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.

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