EGARCH_RESID - EGARCH fitted values of standardized residuals

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

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 number of gamma-coefficients must match the number of alpha-coefficients.
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.
7. The standardized residuals have a mean of zero and a variance of one (1).
8. 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

• 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.