# 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 is 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.

## Examples

Example 1:

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
A B C D E
Date Data EGARCH_RESID
January 10, 2008 -2.827 -2.152 EGARCH(1,1)
January 11, 2008 -0.947 -1.095 Mean -0.266
January 12, 2008 -0.877 -0.688 Alpha_0 1.583
January 13, 2008 1.209 1.087 Alpha_1 -1.755
January 14, 2008 -1.669 -1.879 Gamma_1 0.286
January 15, 2008 0.835 1.857 Beta_1 0.470
January 16, 2008 -0.266 0.000
January 17, 2008 1.361 1.527
January 18, 2008 -0.343 -0.190
January 19, 2008 0.475 0.578
January 20, 2008 -1.153 -0.687
January 21, 2008 1.144 0.871
January 22, 2008 -1.070 -0.777
January 23, 2008 -1.491 -0.888
January 24, 2008 0.686 0.647
January 25, 2008 0.975 0.974
January 26, 2008 -1.316 -1.274
January 27, 2008 0.125 0.431
January 28, 2008 0.712 0.755
January 29, 2008 -1.530 -1.188
January 30, 2008 0.918 1.097
January 31, 2008 0.365 0.952
February 1, 2008 -0.997 -1.177
February 2, 2008 -0.360 -0.111
February 3, 2008 1.347 0.849
February 4, 2008 -1.339 -0.937
February 5, 2008 0.481 0.571
February 6, 2008 -1.270 -0.764
February 7, 2008 1.710 1.271
February 8, 2008 -0.125 0.218
February 9, 2008 -0.940 -0.479