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
- The underlying model is described here.
- The time series is homogeneous or equally spaced.
- The time series may include missing values (e.g. #N/A) at either end.
- The number of gamma-coefficients must match the number of alpha-coefficients.
- The number of parameters in the input argument - alpha - determines the order of the ARCH component model.
- The number of parameters in the input argument - beta - determines the order of the GARCH component model.
- The standardized residuals have a mean of zero and a variance of one (1).
- 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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Files Examples
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
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