# GARCH_RESID - GARCH fitted values of standardized residuals

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

## Syntax

GARCH_RESID(X, Order, mean, alphas, 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 GARCH model mean (i.e. mu).
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 Description
1 (default) Gaussian or Normal Distribution
2 Student's t-Distribution
3 Generalized Error Distribution (GED)
v
is the shape factor (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 standardized residuals have a mean of zero and a variance of one (1).
5. The GARCH model's standardized residuals is defined as:
$$\epsilon_t = \frac{a_t}{\sigma_t}$$
$$a_t = x_t - \mu$$
Where:
• $\epsilon$ is the GARCH model's standardized residual at time t.
• $a_t$ is the GARCH model's residual at time t.
• $x_t$ is the value of the time series at time t.
• $\mu$ is the GARCH mean.
• $\sigma_t$ is the GARCH conditional volatility at time t.
6. The number of parameters in the input argument - alpha - determines the order of the ARCH component model.
7. 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 GARCH_RESID
January 10, 2008 -2.827 -2.669 GARCH(1,1)
January 11, 2008 -0.947 -0.788 Mean -0.16
January 12, 2008 -0.877 -0.718 Alpha_0 0.608
January 13, 2008 1.209 1.370 Alpha_1 0.00
January 14, 2008 -1.669 -1.510 Beta_1 0.391
January 15, 2008 0.835 0.996
January 16, 2008 -0.266 -0.106
January 17, 2008 1.361 1.522
January 18, 2008 -0.343 -0.183
January 19, 2008 0.475 0.636
January 20, 2008 -1.153 -0.994
January 21, 2008 1.144 1.305
January 22, 2008 -1.070 -0.911
January 23, 2008 -1.491 -1.332
January 24, 2008 0.686 0.847
January 25, 2008 0.975 1.136
January 26, 2008 -1.316 -1.157
January 27, 2008 0.125 0.285
January 28, 2008 0.712 0.873
January 29, 2008 -1.530 -1.371
January 30, 2008 0.918 1.079
January 31, 2008 0.365 0.525
February 1, 2008 -0.997 -0.838
February 2, 2008 -0.360 0.200
February 3, 2008 1.347 1.508
February 4, 2008 -1.339 -1.180
February 5, 2008 0.481 0.642
February 6, 2008 -1.270 -1.111
February 7, 2008 1.710 1.872
February 8, 2008 -0.125 0.035
February 9, 2008 -0.940 -0.781