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    

Files Examples

References

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