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

## Syntax

**EGARCH_RESID**(**X**, **Order**, **mean**, **alphas**, **gammas**, **betas**, **innovation**, **v**)

- 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 E-GARCH model mean (i.e., mu).
- alphas
- are the parameters of the ARCH(p) component model (starting with the lowest lag).
- gammas
- are the leverage parameters (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 model for the innovations/residuals (1 = Gaussian (default), 2 = t-Distribution, 3 = GED).
value Description 1 Gaussian or Normal Distribution (default). 2 Student's t-Distribution. 3 Generalized Error Distribution (GED). - v
- is the shape parameter (or degrees of freedom) of the innovations/residuals probability distribution function.

## 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 number of gamma-coefficients must match the number of alpha-coefficients.
- 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.
- The standardized residuals have a mean of zero and a variance of one (1).
- The E-GARCH model's standardized residuals are defined as: $$\epsilon_t = \frac{a_t}{\sigma_t} $$ $$a_t = x_t - \mu $$ Where:
- $\epsilon $ is the E-GARCH model's standardized residual at time $t$.
- $a_t$ is the E-GARCH model's residual at time $t$.
- $x_t$ is the value of the time series at time $t$.
- $\mu$ is the E-GARCH mean.
- $\sigma_t$ is E-GARCH conditional volatility at time $t$.

## 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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