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:

 
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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    

Files Examples

References

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